Fourier-Laplace transforms and the Bergman spaces
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- by Saburou Saitoh PDF
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Abstract:
The Fourier-Laplace transforms on ${R^n}(n \geq 2)$ whose images belong to the Bergman spaces are investigated from the point of view of a general theory of integral transforms. The central problems are to give the expressions of the Bergman kernels in terms of the Fourier-Laplace transforms, and to investigate the relationship between the domains and the ranges in the expressions.References
- N. Aronszajn, La théorie des noyaux reproduisants et ses applications. I, Proc. Cambridge Philos. Soc. 39 (1943), 133–153 (French). MR 8639
- N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337–404. MR 51437, DOI 10.1090/S0002-9947-1950-0051437-7
- Salomon Bochner and William Ted Martin, Several Complex Variables, Princeton Mathematical Series, vol. 10, Princeton University Press, Princeton, N. J., 1948. MR 0027863
- B. A. Fuks, Theory of analytic functions of several complex variables, American Mathematical Society, Providence, R.I., 1963. Translated by A. A. Brown, J. M. Danskin and E. Hewitt. MR 0168793
- B. A. Fuks, Special chapters in the theory of analytic functions of several complex variables, Translations of Mathematical Monographs, Vol. 14, American Mathematical Society, Providence, R.I., 1965. Translated from the Russian by A. Jeffrey and N. Mugibayashi. MR 0188477 T. G. Genchev, Some theorems of Paley-Wiener’s type, Complex Analysis and Applications 83, Sofia, 1985. —, Paley-Wiener type theorem for functions in Bergman spaces over tube domains, J. Anal. Appl. (to appear).
- S. G. Gindikin, Integral formulas for Siegel domains of second kind, Dokl. Akad. Nauk SSSR 141 (1961), 531–534 (Russian). MR 0132207 —, Analytic functions in tubelar regions, Soviet Math. Dokl. 3 (1962), 1178-1183. I. S. Gradshleyn and I. M. Ryzhik, Tables of integrals, series and product, Academic Press, New York, 1980.
- L. K. Hua, Harmonic analysis of functions of several complex variables in the classical domains, American Mathematical Society, Providence, R.I., 1963. Translated from the Russian by Leo Ebner and Adam Korányi. MR 0171936
- Saburou Saitoh, Integral transforms in Hilbert spaces, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), no. 8, 361–364. MR 683264
- Saburou Saitoh, Hilbert spaces induced by Hilbert space valued functions, Proc. Amer. Math. Soc. 89 (1983), no. 1, 74–78. MR 706514, DOI 10.1090/S0002-9939-1983-0706514-9
- S. Saitoh, A general theory of integral transforms and its applications, Mat. Vesnik 37 (1985), no. 1, 121–133 (English, with Serbo-Croatian summary). International symposium on complex analysis and applications (Arandjelovac, 1984). MR 791576 —, The Laplace transform of ${L_p}$ functions with weights, Appl. Anal. 22 (1986), 103-109.
- Friedrich Sommer and Johannes Mehring, Kernfunktion und Hüllenbildung in der Funktionentheorie mehrerer Veränderlichen, Math. Ann. 131 (1956), 1–16 (German). MR 77650, DOI 10.1007/BF01354662
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 985-992
- MSC: Primary 32A35; Secondary 42A38, 42B05, 44A10
- DOI: https://doi.org/10.1090/S0002-9939-1988-0934879-6
- MathSciNet review: 934879