On the solutions of a convolution equation in a semi-strip

V. Dilnyi

We consider a convolution type equation for the Smirnov spaces in a semi-strip. An esti- mation of a solution in terms of analytic extension is obtained.

1. P. Koosis, Introduction to Hp spaces, Second edition. Cambridge Tracts in Mathematics, V.115, Cambridge University Press, Cambridge, 1998.

2. A. Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math., 81 (1949), 239–255.

3. P. Lax, Translation invariant subspaces, Acta Math., 101 (1959), 163–178.

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

5. B. Vinnitsky, Solutions of gomogeneous convolution equation in one class of functions analytical in a semistrip, Mat. Stud., 7 (1997), №1, 41–52.

6. B. Vinnitsky, V. Dil’nyi, On extension of Beurling-Lax theorem, Math. Notes, 79 (2006), 362–368.

7. V. Dilnyi, On cyclic functions in weighted Hardy spaces, Journ. of Math. Phys., Anal., Geom., 7 (2011), 19–33.

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

	On the solutions of a convolution equation in a semi-strip
Author	V. Dilnyi dilnyi@ukr.net Ivan Franko National University of Lviv
Abstract	We consider a convolution type equation for the Smirnov spaces in a semi-strip. An esti- mation of a solution in terms of analytic extension is obtained.
Keywords	Hardy space; convolution equation; translation invariant subspaces
Reference	1. P. Koosis, Introduction to Hp spaces, Second edition. Cambridge Tracts in Mathematics, V.115, Cambridge University Press, Cambridge, 1998. 2. A. Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math., 81 (1949), 239–255. 3. P. Lax, Translation invariant subspaces, Acta Math., 101 (1959), 163–178. 4. B. Vinnitskii, On zeros of functions analytic in a half plane and completeness of systems of exponents, Ukr. Math. Jour., 46 (1994), 484–500. 5. B. Vinnitsky, Solutions of gomogeneous convolution equation in one class of functions analytical in a semistrip, Mat. Stud., 7 (1997), №1, 41–52. 6. B. Vinnitsky, V. Dil’nyi, On extension of Beurling-Lax theorem, Math. Notes, 79 (2006), 362–368. 7. V. Dilnyi, On cyclic functions in weighted Hardy spaces, Journ. of Math. Phys., Anal., Geom., 7 (2011), 19–33. 8. I. Privalov, Randeigenschaften analytischer Funktionen, VEB Deutscher Verlag Wiss, Berlin, 1956.
Pages	61-66
Volume	42
Issue	1
Year	2014
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html