On equivalence for subspaces of one weighted Hardy space

V.Dilnyi

Equivalence is established of subspaces of one exponential-weighted space Hardy in half-plane and of classes of entire functions belonging to $L^2$ on all half-lines with the exception of a semi-strip.

1. Benedetto J., Heinig H. Weighted Hardy spaces and the Laplace transform, Lect. Notes. Math., 992 (1983), 240-277.

2. Fedoryuk M.V. Asymptotics: integrals and sums, Nauka, Moskow, 1987 (Russian).

3. Koosis P. Introduction to $H^p$ spaces. Second edition. Cambridge Tracts in Mathematics, 115, Cambridge University Press, Cambridge, 1998.

4. Levin B., Lyubarskii Yu. Interpolation by mean of entire functions from special classes and expansions in series of exponentials, Izvestiya Acad. Sci. USSR, ser. Mathematics, 39 (1975), 657-702 (Russian, English translation in Soviet Mathematics, Izvestiya)

5. Martyrosian V. On a theorem of Djrbashian of the Phragmen-Lindelof type // Math. Nachr., 144 (1989), 21-27.

6. Nikolskii N.~K. Treatise on the shift operator. Spectral function theory, Springer-Verlag, Berlin, 1986

7. Paley R.E.A.C., Wiener N. Fourier transforms in complex domain (AMS Colloq. Publ. XIX). Providence:AMS, 1934, 184~pp.

8. Privalov I. Randeigenschaften analytischer Functionen, VEB Deutscher Verlag Wiss., Berlin, 1956.

9. Rooney P. A generalization of the Hardy spaces, Can. J. Math. 16 (1964), 358-369.

10. Sedletskii A.~M. Equivalent definition of the Hardy spaces a half-plane and some offers, Math. USSR Sb., 96 (1975), 75-82.

11. Vinnitskii B., Dil'nyi V. On extension of Beurling-Lax theorem, Math. Notes, 79 (2006), 362-368.

12. Vinnitskii B. On zeros of functions analytic in a half plane and completeness of systems of exponents, Ukr. Math. Jour. 46 (1994), 484-500.

13. Vinnitsky B. An extension of Paley-Wiener theorem, Mat. Stud., 4 (1995), 37-44 (Ukrainian)

14. Vynnytskyi B. On zeros of some classes of functions analytic in half-plane, Mat. Stud., 6 (1996), 67-72. (Ukrainian)

15. Vynnyts'kyi B., Dil'nyi V. On solutions of homogeneous convolution equation generated by singularity, Mat. Stud., 19 (2003), 149-155.

	On equivalence for subspaces of one weighted Hardy space
Author	V.Dilnyi dilnyi@ukr.net Drohobych Ivan Franko State University, Institute of Physics, Mathematics and Informatics
Abstract	Equivalence is established of subspaces of one exponential-weighted space Hardy in half-plane and of classes of entire functions belonging to $L^2$ on all half-lines with the exception of a semi-strip.
Keywords	one-exponential weighted Hardy space, entire function, half-line, semi-strip
DOI	doi:10.30970/ms.33.1.71-77
Reference	1. Benedetto J., Heinig H. Weighted Hardy spaces and the Laplace transform, Lect. Notes. Math., 992 (1983), 240-277. 2. Fedoryuk M.V. Asymptotics: integrals and sums, Nauka, Moskow, 1987 (Russian). 3. Koosis P. Introduction to $H^p$ spaces. Second edition. Cambridge Tracts in Mathematics, 115, Cambridge University Press, Cambridge, 1998. 4. Levin B., Lyubarskii Yu. Interpolation by mean of entire functions from special classes and expansions in series of exponentials, Izvestiya Acad. Sci. USSR, ser. Mathematics, 39 (1975), 657-702 (Russian, English translation in Soviet Mathematics, Izvestiya) 5. Martyrosian V. On a theorem of Djrbashian of the Phragmen-Lindelof type // Math. Nachr., 144 (1989), 21-27. 6. Nikolskii N.~K. Treatise on the shift operator. Spectral function theory, Springer-Verlag, Berlin, 1986 7. Paley R.E.A.C., Wiener N. Fourier transforms in complex domain (AMS Colloq. Publ. XIX). Providence:AMS, 1934, 184~pp. 8. Privalov I. Randeigenschaften analytischer Functionen, VEB Deutscher Verlag Wiss., Berlin, 1956. 9. Rooney P. A generalization of the Hardy spaces, Can. J. Math. 16 (1964), 358-369. 10. Sedletskii A.~M. Equivalent definition of the Hardy spaces a half-plane and some offers, Math. USSR Sb., 96 (1975), 75-82. 11. Vinnitskii B., Dil'nyi V. On extension of Beurling-Lax theorem, Math. Notes, 79 (2006), 362-368. 12. Vinnitskii B. On zeros of functions analytic in a half plane and completeness of systems of exponents, Ukr. Math. Jour. 46 (1994), 484-500. 13. Vinnitsky B. An extension of Paley-Wiener theorem, Mat. Stud., 4 (1995), 37-44 (Ukrainian) 14. Vynnytskyi B. On zeros of some classes of functions analytic in half-plane, Mat. Stud., 6 (1996), 67-72. (Ukrainian) 15. Vynnyts'kyi B., Dil'nyi V. On solutions of homogeneous convolution equation generated by singularity, Mat. Stud., 19 (2003), 149-155.
Pages	71-77
Volume	33
Issue	1
Year	2010
Journal	Matematychni Studii
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