New results on the invertibility of the finite interval convolution operator

被引：3

作者：

Lopes, PA ^{[1
]}

dos Santos, AF ^{[1
]}

机构：

[1] Univ Tecn Lisboa, Dept Matemat, Inst Super Tecn, P-1096 Lisbon, Portugal

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2000年 / 38卷 / 03期

关键词：

D O I：

10.1007/BF01291717

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Conditions for the invertibility and explicit formulas for the inverse of the convolution operator on a finite interval are obtained making use of solutions of corona problems. Using these results, a family of classes of functions is defined for which the study of invertibility can be carried through. An example of one class of this family is presented and a smaller class, for which the calculations are simpler, is more thoroughly studied.

引用

页码：317 / 333

页数：17

共 50 条

[1] New results on the invertibility of the finite interval convolution operator
P. A. Lopes
A. F. dos Santos
Integral Equations and Operator Theory, 2000, 38 : 317 - 333
[2] A new approach to the convolution operator on a finite interval
Lopes, PA
dosSantos, AF
INTEGRAL EQUATIONS AND OPERATOR THEORY, 1996, 26 (04) : 460 - 475
[3] CONVOLUTION OPERATOR ON A FINITE INTERVAL
LJUBARSKII, JI
MATHEMATICS OF THE USSR-IZVESTIYA, 1977, 11 (03): : 583 - 611
[4] CONVOLUTION-OPERATORS ON A FINITE INTERVAL WITH PERIODIC KERNEL - FREDHOLM PROPERTY AND INVERTIBILITY
BASTOS, MA
DOSSANTOS, AF
INTEGRAL EQUATIONS AND OPERATOR THEORY, 1993, 16 (02) : 186 - 223
[5] INVERTIBILITY OF TOEPLITZ OPERATOR DOES NOT IMPLY ITS INVERTIBILITY BY FINITE SECTION METHOD
TREIL, SR
DOKLADY AKADEMII NAUK SSSR, 1987, 292 (03): : 563 - 567
[6] On eigenfunctions of a convolution operator on a finite interval for which the Fourier image of the kernel is the characteristic function
Polosin, A. A.
DOKLADY MATHEMATICS, 2017, 96 (01) : 389 - 392
[7] ASYMPTOTICS OF CONVOLUTION OPERATOR SPECTRUM AND EIGENFUNCTIONS AT A FINITE INTERVAL WITH FOURIER HOMOGENOUS TRANSFORMATION OF KERNEL
PALTSEV, BV
DOKLADY AKADEMII NAUK SSSR, 1974, 218 (01): : 28 - 31
[8] On eigenfunctions of a convolution operator on a finite interval for which the Fourier image of the kernel is the characteristic function
A. A. Polosin
Doklady Mathematics, 2017, 96 : 389 - 392
[9] Spectrum and eigenfunctions of the convolution operator on a finite interval with kernel whose transform is a characteristic function
Polosin, A. A.
DIFFERENTIAL EQUATIONS, 2017, 53 (09) : 1145 - 1159
[10] Spectrum and eigenfunctions of the convolution operator on a finite interval with kernel whose transform is a characteristic function
A. A. Polosin
Differential Equations, 2017, 53 : 1145 - 1159

← 1 2 3 4 5 →