Abstract

In this paper, we study some properties of a class of integral operators that depends on the cosine and sine Fourier trans-forms. In particular, we will exhibit properties related with their invertibility, the spectrum, Parseval type identities and involutions. Moreover, a new convolution will be proposed and consequent integral equations will be also studied in detail. Namely, we will characterize the solvability of two integral equations which are associated with the integral operator under study. Moreover, under appropriate conditions, the unique solutions of those two equations are also obtained in a constructive way.

Highlights

  • AND BASIC PROPERTIESIntegral operators have a great importance in applications due to their potential use in modeling a huge variety of applied problems

  • We study some properties of a class of integral operators that depends on the cosine and sine Fourier transforms

  • A new convolution will be proposed and consequent integral equations will be studied in detail

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Summary

Introduction

AND BASIC PROPERTIESIntegral operators have a great importance in applications due to their potential use in modeling a huge variety of applied problems. Under appropriate conditions, the unique solutions of those two equations are obtained in a constructive way. There are convolutions somehow associated with the integral operators and allow the consideration of consequent convolution type equations. We say that an algebraic operator K ∈ L(X) is of order m if there does not exist a normed polynomial Q(t) of degree k < m such that Q(K) = 0 on X.

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