GENERAL SOLUTION OF THE HOMOGENEOUS CONVOLUTION EQUATION IN SPACES OF ULTRADIFFERENTIABLE FUNCTIONS

被引：1

作者：

Polyakova, D. A. ^{[1
,2
]}

机构：

[1] Southern Fed Univ, Milchakov Str 8A, Rostov Na Donu 344090, Russia

[2] RAS, Vladikavkaz Sci Ctr, Southern Math Inst, Markus Str 22, Vladikavkaz 362027, Russia

来源：

ST PETERSBURG MATHEMATICAL JOURNAL | 2020年 / 31卷 / 01期

关键词：

Ultradifferentiable functions; convolution equation; differential equation of infinite order; OPERATORS;

D O I：

10.1090/spmj/1587

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An exponential-polynomial basis is constructed in the space of all solutions of a homogeneous convolution equation in the Beurling spaces of ultradifferentiable functions of mean type on the real axis.

引用

页码：85 / 105

页数：21

共 35 条

[1] ON SOLUTIONS OF CONVOLUTION EQUATIONS IN SPACES OF ULTRADIFFERENTIABLE FUNCTIONS
Polyakova, D. A.
ST PETERSBURG MATHEMATICAL JOURNAL, 2015, 26 (06) : 949 - 963
[2] SOLVABILITY OF CONVOLUTION EQUATIONS IN THE BEURLING SPACES OF ULTRADIFFERENTIABLE FUNCTIONS OF MEAN TYPE ON AN INTERVAL
Abanina, D. A.
SIBERIAN MATHEMATICAL JOURNAL, 2012, 53 (03) : 377 - 392
[3] On the Kernels of Convolution Operators in the Roumieu Spaces of Ultradifferentiable Functions
Polyakova, D. A.
SIBERIAN MATHEMATICAL JOURNAL, 2025, 66 (01) : 213 - 224
[4] Solvability of convolution equations in the Beurling spaces of ultradifferentiable functions of mean type on an interval
D. A. Abanina
Siberian Mathematical Journal, 2012, 53 (3) : 377 - 392
[5] Isomorphism between the solution spaces of a discrete convolution equation and a convolution equation on the space of entire functions
Napalkov, V. V.
Kim, V. E.
MATHEMATICAL NOTES, 2006, 80 (5-6) : 692 - 709
[6] Isomorphism between the solution spaces of a discrete convolution equation and a convolution equation on the space of entire functions
V. V. Napalkov
V. É. Kim
Mathematical Notes, 2006, 80 : 692 - 709
[7] Invariant Subspaces in Nonquasianalytic Spaces of Ω-Ultradifferentiable Functions on an Interval
N. F. Abuzyarova
Russian Mathematics, 2023, 67 : 75 - 79
[8] Representation of solutions of convolution equations in nonquasianalytic beurling classes of ultradifferentiable functions of mean type
Abanina D.A.
Russian Mathematics, 2011, 55 (6) : 1 - 8
[9] Invariant Subspaces in Nonquasianalytic Spaces of Ω-Ultradifferentiable Functions on an Interval
Abuzyarova, N. F.
RUSSIAN MATHEMATICS, 2023, 67 (11) : 75 - 79
[10] Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting
Boiti, Chiara
Jornet, David
Oliaro, Alessandro
Schindl, Gerhard
BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2020, 15 (01)

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