PUBLICATIONS

BOOKS

  1. Holomorphic Partial Differential Equations and Classical Potential Theory,
    Universidad de La Laguna Press, 1996, ISBN# 84-600-9323-9. (PDF)
  2. Quadrature Domains and their Applications, co-editor
    (with P. Ebenfelt, B. Gustafsson and M. Putinar),
    Operator Theory Advances and Applications, vol. 156, Birkhäuser, 2005, 277pp., ISBN # 3-7643-7145-5.
  3. Complex and Harmonic Analysis, co-editor
    (with A. Carbery, P. Duren and A. Siskakis),
    Proceedings of the International Conference May 25-27, 2006, Aristotle University of Thessaloniki, DEStech Publications, 2007, 327pp, ISBN #978-1-932078-73-2.
  4. Complex Analysis and Dynamical Systems VI, co-editor, Conference Proceedings (Naharia, 2013), Contemporary Mathematics 653, Amer. Math. Soc., Providence RI, 2015, ISBN 978-1-4704-1653-9.
  5. Complex Analysis and Dynamical Systems VII, co-editor, Conference Proceedings (Naharia, 2015), Contemporary Mathematics 699, Amer. Math. Soc., Providence RI, 2017, ISBN 978-1-4704-2961-4.

ARTICLES

  1. Remarks concerning boundary properties of analytic functions of Ep classes, Indiana Math. J. 31(6) (1982), 779-787.
  2. On a geometric approach to problems concerning Cauchy integrals and rational approximation, Ph D thesis, Brown University, Providence, RI, 1983, 120pp.(PDF)
  3. Factorization theorems for certain classes of analytic functions in multiply connected domains, Pacific J. Math. 108(2) (1983), 295-318.
  4. Sets of finite perimeter, Cauchy integrals and rational approximation, Approximation Theory IV, Academic Press, C. Chui, L. Schumaker and J. Ward (eds.), pp. 567-573.
  5. Annihilating measures of the algebra R (X), J. Funct. Anal. 58(2) (1984), 175-193.
  6. On removal of periods of conjugate functions in multiply connected domains, Mich. Math. J. 31 (1984), 371-379.
  7. The Cauchy-Green formula and rational approximation on the sets with a finite perimeter in the complex plane, J. Funct. Anal. 64(1) (1985), 112-123.
  8. A note on Toeplitz operators, Lecture Notes in Math., vol. 1166, Geometry of Banach spaces, N. Kalton and E. Saab (eds.), June 24-29, 1984, pp. 89-95, Springer-Verlag, 1985.
  9. On an extremal problem in the theory of rational approximation, J. of Approximation Theory 50(2) (1987), 127-132 (with D. Luecking).
  10. Smirnov classes of analytic functions in multiply connected domains, Appendix to English Transl. of S. Ya. Khavinson's Foundations of the theory of extremal problems for bounded analytic functions and their various generalizations, Amer. Math. Soc. Transl. 129 (1986), 57-61.
  11. On a geometric localization of the Cauchy potentials, Mich. Math. J. 33 (1986), 377-385.
  12. Symmetry and uniform approximation by analytic functions, Proc. Amer. Math. Soc. 101(3) (1987), 475-483.
  13. The isoperimetric inequality and rational approximation, Amer. Math. Monthly 96(1) (1989), 18-30 (with T. Gamelin).
  14. On uniform approximation by harmonic functions, Mich. Math. J. 34 (1987), 465-473.
  15. F. and M. Riesz theorem, analytic balayage and problems in rational approximation, Constructive Approximation 4 (1988), 341-356.
  16. Hankel operators in multiply connected domains, Complex Variables 13 (1989), 21-33 (with J. M. Anderson).
  17. Duality and uniform approximation by solutions of elliptic equations, Operator Theory, Advanced and Applications, vol. 35, 1988, pp. 129-141, Birkhäuser.
  18. Remarks on the reflection principle for harmonic functions, J. d'Analyse 54 (1990), 60-76 (with H. S. Shapiro).
  19. The Vekua hull of a plane domain, Complex Variables 14 (1990), 117-128 (with H. S. Shapiro).
  20. Remarks concerning cyclic vectors in Bergman and Hardy spaces, Mich. Math. J. 38 (1991), 191-205 (with J. Akeroyd and H. S. Shapiro).
  21. On reflection of harmonic functions in surfaces of revolution, Complex Variables 17 (1991), 7-14.
  22. Singularities of harmonic functions in Cn, Proc. Symp. Pure and Applied Math., American Mathematical Society, Providence, RI, vol. 52, 1991, Part 3, pp. 207-217.
  23. An extremal problem for harmonic functions in the ball, Canadian Math. Bulletin 35(2) (1992), 218-220.
  24. Contractive zero-divisors in Bergman spaces, Contemporary Mathematics, vol. 137, 1992, pp. 217-220, American Mathematical Society, Providence, RI (with P. Duren, H. S. Shapiro and C. Sundberg).
  25. Remarks concerning spectral properties of some operators arising in potential theory, Quarterly J. Math., 43 (1992), 387-407 (with J. M. Anderson and V. Lomonosov).
  26. Spectral estimates of Cauchy's transform in L2(W), J. Integral Equations and Operation Theory 15 (1992), 901-919 (with J. Arazy).
  27. Dirichlet's problem when the data is an entire function, Bull. London Math. Soc. 24 (1992), 456-468 (with H. S. Shapiro).
  28. Contractive zero divisors in Bergman spaces, Pacific J. Math. 157(1) (1993), 37-56 (with P. Duren, H. S. Shapiro and C. Sundberg).
  29. Analytic continuation and the heat equation: I. Fredholm's first paper, Expositiones Math. 12 (1994), 79-95 (with H. S. Shapiro). (PDF)
  30. Approximation by harmonic vector fields, Houston J. Math. 20(1) (1994), 75-92 (with B. Gustafsson).
  31. Invariant subspaces in Bergman spaces and the biharmonic equation, Mich. Math. J., 41 (1994), 247-259 (with P. Duren, H. S. Shapiro and C. Sundberg).
  32. Invariant subspaces in Bergman spaces and Hedenmalm's boundary value problerm, (with H. S. Shapiro), Arkiv for Math. 32(2) (1994), 309-321.
  33. An isoperimetric problem, Linear and Complex Analysis, Problem Book 3, Part II, V.P. Khavin and N. K. Nikolsky (eds.), Lecture Notes Math., vol. 1574, 1994, pp. 133-135, Springer-Verlag.
  34. A note on entire solutions of the eiconal equation, Amer. Math. Monthly 102(2) (1995), 159-161.
  35. On Dirichlet series with gaps, (with J. M. Anderson and H. S. Shapiro), Revista Math. Iber., Vol. II, 2 (1995), 453-476.
  36. Extremal functions in invariant subspaces of Bergman spaces, (with P. Duren and H. S. Shapiro), Illinois J. Math. 40 (1996), 202-210.
  37. Rectangular parallelepipeds in ellipsoids (with J. Duncan and H. S. Shapiro), SIAM Review 38 (1996), 655-657.
  38. On annihilators of harmonic vector fields (with B. Gustafsson), Zapiski Nauchnych Seminarov POMI 232 (1996), 90-108.
  39. Cauchy's problem for harmonic functions with entire data on a sphere, Bull. Can. Math. Soc. 40 (1) (1997), 60-66.
  40. Analytic continuation of Jacobi polynomial expansions, (with P. Ebenfelt and H. S. Shapiro), Indagationes Math. N. S. 8(1) (1997), 19-31.
  41. Point-to-point reflection of harmonic functions across real analytic hypersurfaces in Rn, (with P. Ebenfelt), J. d'Analyse 68 (1996), 145-182. (PDF)
  42. Boundary correspondence and dilatation of harmonic mappings, (with P. Duren), Complex Variables 33 (1997), 105-112.
  43. Extending solutions of holomorphic partial differential equations across real hypersurfaces , (with P. Ebenfelt and H. S. Shapiro), J. London Math Society 57(2) (1998), 411-432.
  44. The Schwarz potential in Rn and Cauchy's problem for the Laplace equation, TRITA-MAT-1989-36, Royal Institute of Technology, Stockholm, 112 pp. (with H. S. Shapiro). (PDF)
  45. Bohr's power series theorem in several variables, (with H. P. Boas), Proc. Amer. Math. Soc. 125(10) (1997), 2975-2979.
  46. A remark on a paper by T. Qian, Complex Variables 32(4) (1997), 341-344.
  47. Do solid tori have Pompeiu property? (with C. Berenstein), Expositiones Math. 15 (1997), 87-93.
  48. Approximation of continuous functions in L1 norm by elements of a uniform algebra, (with F. Pérez-Gonzàlez & H. S. Shapiro), Constr. Approx. 14 (1998), 401-410.
  49. Certain linear extremal problems in Bergman spaces of analytic functions, (with M. Stessin), Indiana Univ. Math J. 46 (1997), 933-974.
  50. Wandering subspaces in Hardy spaces, (with M. Stessin and T. Lance), Mich. Math J. 44 (1997), 597-606.
  51. Vitae: F. W. Wiener, (with H. Boas), Math. Intellegencer 22(2) (2000), 73-75.
  52. Best approximation in the supremum norm by analytic and harmonic functions, (with H. S. Shapiro), Arkiv for Math. 32(2) (2001), 339-359. (PS)
  53. Extreme Pick-Nevanlinna Interpolants, (with S. Fisher), Can. J., Math. 59 (1999), 977-996.
  54. On approximation in the mean by analytic and harmonic functions, (with H. S. Shapiro and J. McCarthy), Indiana Univ. J. 49(4) (2000), 1981-1513.
  55. A free boundary problem related to single layer potentials, (with P. Ebenfelt and H. S. Shapiro), Ann. Acad. Sci. Fenn., Vol 27, fasc. 1, 2002, pp. 22-46. (PDF)
  56. On a maximal number of zeros of certain harmonic polynomials, (with G. Swiatek), Proc. Amer. Math. Soc. 131(2) (2003), 409-414. (PDF)
  57. An inverse problem for the double layer potential, (with P. Ebenfelt and H. S. Shapiro), Computational Methods and Function Theory 1(2) (2001), 387-402. (PS)
  58. Weak compactness in certain star-shift invariant subspaces, (with J. Akeroyd and H. S. Shapiro), J. of Functional Anal. 202 (2003), 98-122. (PS)
  59. Remarks on the Bohr phenomenon, (with C. Beneteau and A. Dahlner), Comput. Methods Funct. Theory 4(1) (2004), 1-19. (PDF)
  60. On the Number of Zeros of Certain Rational Harmonic Functions, (with G. Neumann), Proc. Amer. Math. Soc. 134(4) (2006), 1077-1085. - Download paper
  61. Algebraic aspects of the Dirichlet problem with rational data, (with P. Ebenefelt and Harold S. Shapiro), Quadrature domains and their applications, Operator Theory Advances and Applications, vol. 156, Birkhäuser, 2005, 151-172. (PDF)
  62. A Note on a Theorem of J. Globevnik, Contemporary Math. Vol. 382 (2005), 227-228. (PDF)
  63. Overdetermined Boundary Value Problems, Quadrature Domains and Applications, (with A. Solynin and D. Vassilev), Comput. Methods Funct. Theory 5(1) (2005), 19-48. (PDF)
  64. Extremal problems for nonvanishing functions in Bergman spaces, (with D. Aharonov, C. Beneteau and H. S. Shapiro), Selected topics in complex analysis, S. Ya. Khavinson Memorial Volume, V. Eiderman and M. Samokhin (eds.), Operator Theory Advances and Applications, vol. 158, Birkhäuser, 2005, 59-86. (PDF)
  65. Smooth functions in star-invariant subspaces, (with K. Dyakonov), Recent Advances in Operator-Related Function Theory, Contemporary Mathematics 393 (2006), 59-66, edited by Alec L. Matheson, Michael I. Stessin, Richard M. Timoney. (PDF)
  66. On Poincare's variational problem in potential theory, (with M. Putinar and Harold S. Shapiro), Arch. Rat. Mech., 185(2007), 143-184. (PDF)
  67. Algebraicity in the Dirichlet problem in the plane with rational data, (with S. R. Bell, P. Ebenfelt and Harold S. Shapiro), Complex Variables and Elliptic Equations, Vol. 52, Nos. 2-3, February-March 2007, 235-244. (PDF)
  68. On the classical Dirichlet problem in the plane with rational data, (with S. R. Bell, P. Ebenfelt and Harold S. Shapiro), J. d'Analyse, 100(2006), 157-190. (PDF)
  69. The isoperimetric inequality via approximation theory and free boundary problems, (with Catherine Beneteau), Comput. Methods Funct. Theory 6(2) (2006), 253-274. (PDF)
  70. Approximating $\overline{z}$ in Bergman and Hardy norms, (with Zdenka Guadarrama), Banach Spaces of Analytic Functions, Contemporary Mathematics,Volume 454, 2008, 43-61, edited by Rita A. Hibschweiler and Thomas H. MacGregor. (PDF)
  71. On a uniqueness property of harmonic functions, (with Harold S. Shapriro), Comput. Methods in Function Theory, Volume 8 (2008), Number 1, 143-150. (PDF)
  72. A survey of certain extremal problems for non-vanishing analytic functions, (with Catherine Beneteau), Proceedings of the Conference in Complex and Harmonic Analysis (Thessaloniki, May 2006), DIStech Publications, 2007, 45-61. (PDF)
  73. Robert Jentzsch, mathematician and poet, (with Peter Duren and Anne-Katrin Herbig), Math. Intelligencer, Volume 30 (2008), No. 3, pp. 18-24.
  74. Gravitational lensing by elliptical galaxies and the Schwarz function, (with C. D. Fassnacht and C. R. Keeton), ``Analysis and Mathematicsl Physics'', Proceedings of the Conference on New Trends in Complex and Harmonic Analysis,Voss 2007,edited by B. Gustafsson and A. Vasil’ev, arXiv:0708.2684v1 [math-ph], http://arxiv.org/abs/0708.2684, Burkhäuser, 2009, 115-129. (PDF)
  75. From the fundamental theorem of algebra to astrophysics: a ''harmonious'' path, (with G. Neumann), Notices Amer. Math. Soc., Vol. 55, Issue 6, 2008, 666 - 675.(PDF)
  76. Planar elliptic growth, (with M. Mineev-Weinstein and M. Putinar), Complex Analysis and Operator Theory, 2009, Vol. 3, No. 2, 425-451, http://dx.doi.org/10.1007/s11785-008-0093-7. (PDF)
  77. Robert Jentzsch, mathematiker und poet, (with P. Duren and A.-K. Herbig), Mitteilungen Deutschen Mathematiker-Vereinigung, Band 16, Heft 4 (2008), 233-240.
  78. The search for singularities of solutions to the Dirichlet problem: recent developments, (with E. Lundberg), Centre de Recherches Mathématiques, CRM Proceedings and Lecture Notes, v. 51, 2010, 121-132.(PDF)
  79. Transcendental harmonic mappings and gravitational lensing by isothermal galaxies, (with E. Lundberg), Complex Analysis and Operator Theory, Vol. 4, Issue 3 (2010), 515-524.(PDF)
  80. Recurrence relations for orthogonal polynomials and algebraicity of solutions of the Dirichlet problem, (with N. Stylianopoulos), in "Around the Research of Vladimir Maz'ya II, Partial Differential Equations", pp. 219-228, International Mathematical Series, Vol. 12, ed. by A. Laptev, Springer, 2010.(PDF)
  81. Linearization models for parabolic dynamical systems via Abel's functional equation, (with M. Elin, S. Reich and D. Shoikhet)), Ann. Acad. Sci. Fenn. Ser. Ser A I, Math., Vol. 35, 2010, 1 - 34, http://arxiv.org/abs/0907.2571, (PDF)
  82. Malmheden's theorem revisited, (with M. Agranovsky and H. S. Shapiro), 2009, http://arxiv.org/PS_cache/arxiv/pdf/0908/0908.1837v2.pdf, 22 pp., Expositiones Math., 28(2010), 337 - 350.(PDF)
  83. Lemniscates do not survive Laplacian growth, (with M. Mineev-Weinstein, M. Putinar and R. Teodorescu), 2009, http://arxiv.org/abs/0912.2129, 9 pp., Mathematical Research Letters, 17(2010), no. 2, 335 - 341.(PDF)
  84. Two-dimensional shapes and lemniscates, (with P. Ebenfelt and H. S. Shapiro), Complex analysis and dynamical systems IV. Part 1, 45–59, Contemp. Math., 553, Amer. Math. Soc., Providence, RI, 2011, (PDF), http://arxiv.org/abs/1003.4567
  85. A remark on "Gravitaional lensing and the maximal number of images'': 5 radial objects can lens 27 images,, (with E. Lundberg), 2010, (PDF), 4pp.
  86. Borcea's variance conjectures on the critical points of polynomials, (with R.Pereira, M. Putinar, E. Saff and S. Shimorin), in Notions of Positivity and the Geometry of Polynomials, Series: Trends in Mathematics, Birkhäuser, Basel, pp. 283 – 309, (PDF), http://arxiv.org/PS_cache/arxiv/pdf/1010/1010.5167v1.pdf
  87. Gravitational lensing by a collection of objects with radial densities, (with E. Lundberg), 2011,(PDF), Analysis and Mathematical Physics, 2011, Volume 1, Numbers 2-3, 139- 145.
  88. Analytic functions in Smirnov classses E^p with real boundary values, (with L. De Castro), 2011,(PDF), 6 pp., Complex Analysis and Operator Theory, volume 7, No.1 (2013), 101 - 106.
  89. A survey of linear extremal problems in analytic function spaces, (with C. Beneteau), Centre de Recherches Mathematiques, CRM Proceedings and Lecture Notes, Vol. 55 (2012), 33 - 46. (PDF)
  90. An overdetermined problem in potential theory, (with E. Lundberg and R. Teodorescu), 2012, 18 pp., Pacific J. Math., v. 265, No.1 (2013),85-111, (PDF)
  91. Analytic functions in Smirnov classes E^p with real boundary values II, (with L. De Castro), Analysis and Mathematical Physics, Vol. 3 Issue 1 (2013), 21 - 35. (PDF)
  92. Boundary behaviour of universal Taylor series, (with S. J.Gardiner),2013, 8 pp., Comptes Rendus Mathematique, , Ser I., 352 (2014), 99 - 103. (PDF)
  93. A tale of ellipsoids in potential theory, (with E. Lundberg), 2013, 19 pp., (PDF), Notices of the Amer. Math. Soc., 61(2014), No.2, 148 - 155.
  94. Menahem Max Schiffer, Selected Papers, Vols. 1&2, ed. by P. L. Duren and L. Zalcman, Commentaries, pp. 202, 234, 258, 455. Burkhäuser, 2013.
  95. Extremal domains for self-commutators in the Bergman space, (with M. Fleeman), 2013, 10 pp., Complex Analysis and Operator Theory, Vol. 9, No. 1 (2015), 99-111. (PDF), http://arxiv.org/abs/1311.1842.
  96. Selected problems in classical function theory, (with C. Beneteau), 2014, 11 pp., Centre de Recherches Mathematiques, CRM Proceedings and Lecture Notes, Contemp. Math., v.638 (2015), 255-265.(PDF).
  97. Problems for polynomials of one and several variables, Workshop on Dirichlet spaces and function theory in polydisks, Oberwolfach, 2014, 3 pp., (PDF).
  98. Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems, by G. Kresin and V. Maz'ya, a book review, Bulletin of the AMS, v. 51, No.4 (2014), 701 - 704..
  99. Sun Hong Rhie: an Obituary, (with D. Bennett), Physics Today 67(3), 64(2014), http://dx.doi.org/10.1063/PT.3.2318
  100. A note on the spectral area of Toeplitz operators, (with Ch. Chu), Proc. Amer. Math. Soc., Vol.144, No.6 (2016), 2533 – 2537. (PDF).
  101. Zeros of harmonic polynomials, critical lemniscates and caustics, (with S.- Y. Lee and A. Saez), 2015, 18pp. (PDF), http://arxiv.org/abs/1508.04439.
  102. Approximating z* in the Bergman space, (with M. Fleeman), Recent Progress on Operator Theory and Approximation in Spaces of Analytic Functions, Conference on Completeness Problems, Carleson Measures, and Spaces of Analytic Functions, Institut Mittag-Leffler, Djursholm, Sweden, eds. C. Beneteau et al., Contemporary Math., 679, 2016, 79-90. (PDF), http://arxiv.org/abs/1509.01370 .
  103. Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants, (with C. Beneteau, C. Liaw, D. Seco and A. Sola), 22pp., preprint, 2015, J. London Math.Soc., (2016) 94 (3): 726-746. (PDF).
  104. Dirchlet's problem with entire data posed on an ellispoidal cylinder, (with E. Lundberg and H. Render), 7pp., http://arxiv.org/abs/1602.02837, Potential Analysis, 46(2017), No.1, 55-62.(PDF).
  105. Polynomial lemniscates and their fingerprints: from geometry to topology, (with A. Frolova and A. Vasil'ev), preprint, 2017, 27 pp., (PDF).
  106. An asymptotic Gauss-Lucas theorem, (with R. Bogvad and B. Shapiro, 4pp., preprint, 2015, (PDF), http://arxiv.org/pdf/1510.02339.pdf
  107. A free boundary problem associated with the isoperimetric inequality, (with A. Abanov, C. Beneteau and R. Teodorescu), 2016, preprint, 16pp., (PDF)
  108. The Dirichlet problem for the slab with entire data and a difference equation for harmonic functions, (with E. Lundberg and H. Render), Canadian Math. Bull., 60(2017), no. 1, 146-153, http://arxiv.org/abs/1602.01823, (PDF)
  109. Zeros of optimal polynomial approximants:Jacobi matrices and Jentzsch-type theorems, (with C. Beneteau, C. Liaw, D.Seco and B. Simanek), 2016, 32 pp., http://arxiv.org/pdf/1606.08615v1.pdf
  110. A thought on approximation by bi-analytic functions, 2016, 5 pp., Fields Institute, A Conference in Memory of A. Boivin, accepted.(PDF).
  111. In Memoriam Alexander Vasiliev (1962-2016),(with B.Gustafsson, D. Prokhorov, A.Sergeev and R. Teodorescu), Anal. Math. Physics 7(2017), No.1, 1-8.
  112. Remarks on inner functions and optimal approximants, (with C. Beneteau, M. Fleeman, D. Seco and A. Sola), 2017, 17 pp., Canadian Math. Bulletin, accepted. (PDF).
  113. Questions related to the spectral properties of several classical integral operators and geometry, 2017, 7 pp., CRM Proceedings and Lecture Notes. (PDF).

TRANSLATIONS

  1. S. Ya. Khavinson, Foundations of the theory of extremal problems for bounded analytic functions and their various generalizations, Amer. Math. Soc. Transl. 129 (1986), 1-57.
  2. S. Ya. Khavinson, Extremal problems for analytic functions satisfying additional constraints inside the domain, Amer. Math. Soc. Transl. 129 (1986), 61-114.
  3. K. V. Osipenko, Heinz' problems and optimal extrapolation of analytic functions defined with an error, Math. USSR Sbornik 54(2) (1986), 551-559.
  4. L. R. Volevich and S. G. Gindikin, Convolutors in spaces of distributions and related problems for convolution equations, Selecta Mathematica Sovietica 2 (1), 9-50, Birkhäuser 1982.
  5. V. S. Azarin, On the regularity of the growth of Fourier coefficients of the logarithm of the modulus of an entire function, Selecta Mathematica Sovietica 2 (1) 51-63, Birkhäuser 1982.
  6. F. G. Nasibov, On extremal problems in the classes Ba, Soviet Math. Dokl. 35 (3) (1987), 512-515.
  7. Encyclopedia of Mathematical Sciences, Volume 15, Commutative Harmonic Analysis I, Springer-Verlag, 1991, 268 pp.
  8. S. Ya. Khavinson, Approximation by Linear Superpositions, American Mathematical Society Translations 159 (1996), 190 pp.

Works in Progress

  1. Holomorphic Partial Differential Equations and Classical Potential theory, (with E. Lundberg), a monograph in preparation.
  2. Isoperimetric Sandwiches and Approximation by Analytic and Harmonic Functions, (with C. Beneteau), a monograph in preparation.
  3. Extremal domains for the analytic content, (with A. Abanov, C. Beneteau and R. Teodorescu), in preparation.