The Poincaré inequality and entire functions
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- by J. Michael Pearson PDF
- Proc. Amer. Math. Soc. 118 (1993), 1193-1197 Request permission
Abstract:
Inequalities for spaces of entire functions on ${{\mathbf {C}}^n}$, which generalize the Poincaré inequality for Gaussian measure, are obtained. The relationship between these inequalities and hypercontractive estimates for diffusion semigroups are discussed.References
- V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Comm. Pure Appl. Math. 14 (1961), 187–214. MR 157250, DOI 10.1002/cpa.3160140303
- William Beckner, Sobolev inequalities, the Poisson semigroup, and analysis on the sphere $S^n$, Proc. Nat. Acad. Sci. U.S.A. 89 (1992), no. 11, 4816–4819. MR 1164616, DOI 10.1073/pnas.89.11.4816
- William Beckner, A generalized Poincaré inequality for Gaussian measures, Proc. Amer. Math. Soc. 105 (1989), no. 2, 397–400. MR 954373, DOI 10.1090/S0002-9939-1989-0954373-7
- Leonard Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), no. 4, 1061–1083. MR 420249, DOI 10.2307/2373688
- Svante Janson, On hypercontractivity for multipliers on orthogonal polynomials, Ark. Mat. 21 (1983), no. 1, 97–110. MR 706641, DOI 10.1007/BF02384302
- Carl E. Mueller and Fred B. Weissler, Hypercontractivity for the heat semigroup for ultraspherical polynomials and on the $n$-sphere, J. Functional Analysis 48 (1982), no. 2, 252–283. MR 674060, DOI 10.1016/0022-1236(82)90069-6
- Edward Nelson, The free Markoff field, J. Functional Analysis 12 (1973), 211–227. MR 0343816, DOI 10.1016/0022-1236(73)90025-6
- J. Michael Pearson, A hypercontractive estimate for the heat semigroup on $\textbf {P}^2$, Michigan Math. J. 37 (1990), no. 3, 439–446. MR 1077327, DOI 10.1307/mmj/1029004201
- I. E. Segal, Foundations of the theory of dynamical systems of infinitely many degrees of freedom. I, Mat.-Fys. Medd. Danske Vid. Selsk. 31 (1959), no. 12, 39 pp. (1959). MR 112626
- Irving E. Segal, Mathematical problems of relativistic physics, Lectures in Applied Mathematics (Proceedings of the Summer Seminar, Boulder, Colorado, vol. 1960, American Mathematical Society, Providence, R.I., 1963. With an appendix by George W. Mackey. MR 0144227
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 1193-1197
- MSC: Primary 32A15
- DOI: https://doi.org/10.1090/S0002-9939-1993-1152286-2
- MathSciNet review: 1152286