A Class of Linear Integral Equations and Systems with Sum and Difference Kernel | Zendy

Lothar von Wolfersdorf | Zendy

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A Class of Linear Integral Equations and Systems with Sum and Difference Kernel

Author(s) -

Lothar von Wolfersdorf

Publication year - 2003

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1167

Subject(s) - mathematics , integral equation , holomorphic function , mathematical analysis , resolvent , complex plane , riemann–hilbert problem , daniell integral , cauchy's integral formula , volterra integral equation , lebesgue integration , integral transform , fredholm integral equation , summation equation , riemann integral , fourier integral operator , pure mathematics , cauchy problem , initial value problem , boundary value problem

By means of Fourier transform and Cauchy integral techniques a complete investigation of a class of linear integral equations and corresponding systems of equations of cross-correlation type in the Lebesgue spaces L and L is performed. Integral equations of first and second kind are reduced to explicitly solvable Riemann-Hilbert problems for a holomorphic function in the upper half-plane and the system of equations to conjugacy problems for a sectionally holomorphic function, where in the case of a finite interval also the analytic continuation of the solutions to the lower half-plane can be carried out in explicit way. Further, a resolvent representation of the solution to the integral equation and its adjoint equation is derived.

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