Abstract:
This article investigates analytic solutions of a convolution equation and of systems of two convolution equations with a single unknown function. The characteristic functions of all the convolution operators studied here are entire functions of exponential type. A general representation is determined for solutions of homogeneous and inhomogeneous equations and of systems of such equations in the form of absolutely convergent series in entire functions (as a rule, exponentials forming an absolutely representing system). A criterion is established for solvability of a system of two inhomogeneous convolution equations with a single unknown function. The main results are obtained with the help of nontrivial expansions of zero in convex domains with respect to functions forming an absolutely representing system.
Bibliography: 19 titles.
This publication is cited in the following 14 articles:
S. N. Melikhov, “Coefficients of exponential series for analytic functions and the Pommiez operator”, J. Math. Sci. (N. Y.), 257:2 (2021), 206–245
V. B. Sherstyukov, “Asymptotic properties of entire functions with given laws of distribution of zeros”, J. Math. Sci. (N. Y.), 257:2 (2021), 246–272
Ivanova O.A., Melikhov S.N., “O koeffitsientakh ryadov po funktsiyam mittag-lefflera dlya analiticheskikh funktsii”, Izvestiya vysshikh uchebnykh zavedenii. severo-kavkazskii region. seriya: estestvennye nauki, 2012, no. 6, 20–26
On coefficients of series in mittag–leffler functions for analytic functions
V. B. Sherstyukov, “Representation of the reciprocal of an entire function by series of partial fractions and exponential approximation”, Sb. Math., 200:3 (2009), 455–469
S. N. Melikhov, “Extension of entire functions of completely regular growth and right inverse to the operator of representation of analytic functions by quasipolynomial series”, Sb. Math., 191:7 (2000), 1049–1073
A. B. Mikhailov, “On a two-point problem for a second-order partial differential equation with constant coefficients”, Russian Math. (Iz. VUZ), 43:3 (1999), 79–82
Ryuichi ISHIMURA, “THE CHARACTERISTIC SET FOR DIFFERENTIAL-DIFFERENCE EQUATIONS IN REAL DOMAINS”, Kyushu J. Math., 53:1 (1999), 107
I. F. Krasichkov-Ternovskii, “The fundamental principle for invariant subspaces of analytic functions. I”, Sb. Math., 188:2 (1997), 195–226
Korobeinik Y., “On Analytic - Solutions to the Cauchy-Problem for Parabolic Equations”, Differ. Equ., 30:10 (1994), 1640–1646
Ishimura R. Okada Y., “The Existence and the Continuation of Holomorphic Solutions for Convolution Equations in Tube Domains”, Bull. Soc. Math. Fr., 122:3 (1994), 413–433
Korobeinik Y., Melikhov S., “Linear Continuous Right Inverse for Representation Operator and the Conformal-Mappings”, Dokl. Akad. Nauk, 323:5 (1992), 826–829
Yu. F. Korobeinik, “Description of the general form of nontrivial expansions of zero in exponentials. Applications”, Math. USSR-Izv., 39:2 (1992), 1013–1032
Yu. F. Korobeinik, “Nontrivial expansions of zero in absolutely representing systems. Application to convolution operators”, Math. USSR-Sb., 73:1 (1992), 49–66
Korobeinik I., “On Some Applications of Nontrivial Expansions of Zero in the Theory of Convolution-Operators”, 313, no. 6, 1990, 1324–1328
Citation in format AMSBIB
Contact us: