Abstract
This is a (very) personal outlook on the life and mathematical achievements of Harold S. Shapiro, who has passed away in March of 2021, a few days short of his 93rd birthday. It is based on the author’s long (almost 40 years) collaboration and friendship with Harold; so it might be interpreted as “kaddish”.
Similar content being viewed by others
Data availability
Data sharing is not applicable to this article since no data sets were generated or analyzed.
References
Ebenfelt, P., Khavinson, D., Shapiro, H.S.: An inverse problem for the double layer potential. Comput. Methods Funct. Theory 1(2), 387–401 (2001)
Shapiro, H.S.: The Schwarz Function and Its Generalization to Higher Dimensions. University of Arkansas Lecture Notes in the Mathematical Sciences, vol. 9, p. 108. John Wiley & Sons, Inc., A Wiley-Interscience Publication, New York (1992)
Shapiro, H.S.: Clear thinking will never be out of date. Int. J. Math. Educ. Sci. Technol. 16(2), 301–308 (1985)
Shapiro, H.S.: Topics in Approximation Theory. Lecture Notes in Mathematics, vol. 187. Springer, Berlin-New York (1971)
Shapiro, H.S.: Smoothing and Approximation of Functions. Van Nostrand Reinhold Mathematical Studies, p. 136. Van Nostrand Reinhold Co., New York-Toronto, Ont.-London (1969). Revised and expanded edition of mimiographed notes (Matscience Report No. 55)
Havinson, S.Y.: On an extremal problem of the theory of analytic functions. Usp. Matem. Nauk (N.S.) 4(32), 158–159 (1949)
Rogosinski, W.W., Shapiro, H.S.: On certain extremum problems for analytic functions. Acta Math. 90, 287–318 (1953)
Douglas, R.G., Shapiro, H.S., Shields, A.L.: Cyclic vectors and invariant subspaces for the backward shift operator. Ann. Inst. Fourier (Grenoble) 20(1), 37–76 (1970)
Ross, W.T., Shapiro, H.S.: Generalized Analytic Continuation. University Lecture Series, vol. 25, p. 149. American Mathematical Society, Providence (2002)
Khavinson, D., Shapiro, H.S.: The Schwarz potential in \(\mathbb{R}^n\) and Cauchy’s problem for the Laplace equation. Technical Report TRITA-MAT-1989-36, Royal Institute of Technology, Stockholm (1989)
Khavinson, D., Lundberg, E.: Linear Holomorphic Partial Differential Equations and Classical Potential Theory. Mathematical Surveys and Monographs, vol. 232, p. 214. American Mathematical Society, Providence (2018)
Salem, R., Zygmund, A.: Some properties of trigonometric series whose terms have random signs. Acta Math. 91, 245–301 (1954)
Golay, M.J.E.: Multi-slit spectrometry\(\ast \). J. Opt. Soc. Am. 39(6), 437–444 (1949)
Duren, P.L.: Theory of \(H^{p}\) Spaces. Pure and Applied Mathematics, vol. 38. Academic Press, New York-London (1970)
Hoffman, K.: Banach Spaces of Analytic Functions, p. 216. Dover Publications, Inc., New York (1988). Reprint of the 1962 original
Shapiro, H.S.: Extremal problems for polynomials and power series. Ph.D. dissertation, Massachusetts Institute of Technology (1953). Published by: ProQuest LLC, Ann Arbor, MI. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:0187158
Khavinson, S.Y.: Foundations of the theory of extremal problems for bounded analytic functions and their various generalizations. Am. Math. Soc. Transl. 129, 1–57 (1986)
Khavinson, S.Y.: Extremal problems for analytic functions satisfying additional constraints inside the domain. Am. Math. Soc. Transl. 129, 61–114 (1986)
Garnett, J.B.: Bounded Analytic Functions. Pure and Applied Mathematics, vol. 96, p. 467. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London (1981)
Aharonov, D., Shapiro, H.S., Solynin, A.Y.: A minimal area problem in conformal mapping. II. J. Anal. Math. 83, 259–288 (2001)
Aharonov, D., Shapiro, H.S., Solynin, A.Y.: A minimal area problem in conformal mapping. J. Anal. Math. 78, 157–176 (1999)
Davis, P.J.: The Schwarz Function and its Applications The Carus Mathematical Monographs, no. 17, p. 228. The Mathematical Association of America, Buffalo (1974)
Ebenfelt, P., Gustafsson, B., Khavinson, D., Putinar, M. (eds.): Quadrature Domains and Their Applications. Operator Theory: Advances and Applications, vol. 156, p. 277. Birkhäuser Verlag, Basel (2005). The Harold S. Shapiro anniversary volume, Papers from the conference held at the University of California at Santa Barbara, Santa Barbara, CA, March 2003. https://doi.org/10.1007/b137105
Aharonov, D., Shapiro, H.S.: Domains on which analytic functions satisfy quadrature identities. J. Anal. Math. 30, 39–73 (1976)
Sakai, M.: Regularity of a boundary having a Schwarz function. Acta Math. 166(3–4), 263–297 (1991)
Acknowledgements
The author gratefully acknowledges support from the Simons Foundation.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Khavinson, D. Harold Seymour Shapiro 1928–2021; Life in mathematics, in memoriam. Anal.Math.Phys. 12, 63 (2022). https://doi.org/10.1007/s13324-022-00670-0
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s13324-022-00670-0