Monotone and convex operator functions
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- by Julius Bendat and Seymour Sherman
- Trans. Amer. Math. Soc. 79 (1955), 58-71
- DOI: https://doi.org/10.1090/S0002-9947-1955-0082655-4
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Erratum: Trans. Amer. Math. Soc. 82 (1956), 548.
References
- Serge Bernstein, Sur la définition et les propriétés des fonctions analytiques d’une variable réelle, Math. Ann. 75 (1914), no. 4, 449–468 (French). MR 1511806, DOI 10.1007/BF01563654
- R. P. Boas Jr., Functions with positive derivatives, Duke Math. J. 8 (1941), 163–172. MR 4278 O. Brune, Synthesis of a finite two-terminal network whose driving point impedance is a prescribed function of frequency, Journal of Mathematics and Physics vol. 10 (1931) pp. 191-236.
- Wilhelm Cauer, Untersuchungen über ein Problem, das drei positiv definite quadratische Formen mit Streckenkomplexen in Beziehung setzt, Math. Ann. 105 (1931), no. 1, 86–132 (German). MR 1512706, DOI 10.1007/BF01455810 O. Dobsch, Matrixfunktionen beschränkter Schwankung, Math. Zeit. vol. 43 (1937) pp. 353-388.
- Paul R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity, AMS Chelsea Publishing, Providence, RI, 1998. Reprint of the second (1957) edition. MR 1653399
- Erhard Heinz, Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann. 123 (1951), 415–438 (German). MR 44747, DOI 10.1007/BF02054965
- Fritz Kraus, Über konvexe Matrixfunktionen, Math. Z. 41 (1936), no. 1, 18–42 (German). MR 1545602, DOI 10.1007/BF01180403 K. Löwner, Über monotone Matrixfunktionen, Math. Zeit. vol. 38 (1934) pp. 177-216.
- Charles Loewner, Some classes of functions defined by difference or differential inequalities, Bull. Amer. Math. Soc. 56 (1950), 308–319. MR 38387, DOI 10.1090/S0002-9904-1950-09405-1 B. Nagy, Spectraldarstellung linearen Transformationen des Hilbertschen Raumes, Berlin, Springer, 1942.
- Paul I. Richards, A special class of functions with positive real part in a half-plane, Duke Math. J. 14 (1947), 777–786. MR 22261
- M. S. Robertson, On the coefficients of a typically-real function, Bull. Amer. Math. Soc. 41 (1935), no. 8, 565–572. MR 1563142, DOI 10.1090/S0002-9904-1935-06147-6
- M. S. Robertson, Analytic Functions Star-Like in One Direction, Amer. J. Math. 58 (1936), no. 3, 465–472. MR 1507169, DOI 10.2307/2370963
- Werner Rogosinski, Über positive harmonische Entwicklungen und typisch-reelle Potenzreihen, Math. Z. 35 (1932), no. 1, 93–121 (German). MR 1545292, DOI 10.1007/BF01186552
- J. A. Shohat and J. D. Tamarkin, The Problem of Moments, American Mathematical Society Mathematical Surveys, Vol. I, American Mathematical Society, New York, 1943. MR 0008438
- David Vernon Widder, The Laplace Transform, Princeton Mathematical Series, vol. 6, Princeton University Press, Princeton, N. J., 1941. MR 0005923 E. P. Wigner and L. Eisenbud, Higher angular momenta and long range interaction in resonance reactions, Physical Review vol. 72 (1947) pp. 29-41. E. P. Wigner, Nuclear reactions and level widths, American Journal of Physics vol. 17 (1949) pp. 99-109.
- Eugene P. Wigner, On a class of analytic functions from the quantum theory of collisions, Ann. of Math. (2) 53 (1951), 36–67. MR 39059, DOI 10.2307/1969342
Bibliographic Information
- © Copyright 1955 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 79 (1955), 58-71
- MSC: Primary 46.2X
- DOI: https://doi.org/10.1090/S0002-9947-1955-0082655-4
- MathSciNet review: 0082655