Euler spaces of analytic functions
HTML articles powered by AMS MathViewer
- by James Rovnyak PDF
- Trans. Amer. Math. Soc. 308 (1988), 197-208 Request permission
Abstract:
A formula due to Euler and Legendre is used to construct finite-difference counterparts to the Dirichlet space. The spaces have integral representations and characterizations in terms of area integrals. Their reproducing kernels are logarithms of the reproducing kernels of the Newton spaces, which are counterparts to the Hardy class. A Hilbert space with reproducing kernel \[ \log [(1/\overline w z) \log \;1/(1 - \overline w z)]\] is also shown to exist and to be related to Bernoulli numbers and combinatorial theory.References
- N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337–404. MR 51437, DOI 10.1090/S0002-9947-1950-0051437-7 L. de Branges, Square summable power series, Springer-Verlag (in preparation). A. Erdélyi, et al., Higher transcendental functions, vol. 1, McGraw-Hill, New York, 1953. C. Jordan, Calculus of finite differences, 3rd ed., Chelsea, New York, 1979.
- C. Markett, M. Rosenblum, and J. Rovnyak, A Plancherel theory for Newton spaces, Integral Equations Operator Theory 9 (1986), no. 6, 831–862. MR 866967, DOI 10.1007/BF01202519 N. Nielsen, Handbuch der Theorie der Gammafunktion, Chelsea, New York, 1965. N. E. Nörlund, Vorlesungen über Differenzenrechnung, Chelsea, New York, 1954.
- Raymond E. A. C. Paley and Norbert Wiener, Fourier transforms in the complex domain, American Mathematical Society Colloquium Publications, vol. 19, American Mathematical Society, Providence, RI, 1987. Reprint of the 1934 original. MR 1451142, DOI 10.1090/coll/019
- 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
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 308 (1988), 197-208
- MSC: Primary 30H05; Secondary 44A15, 46E20
- DOI: https://doi.org/10.1090/S0002-9947-1988-0929669-9
- MathSciNet review: 929669