IJPAM: Volume 93, No. 3 (2014)

ON AN INHOMOGENEOUS BOUNDARY VALUE PROBLEM
WITH SHIFT INTO THE REGION FOR
THE CAUCHY-RIEMANN EQUATIONS WITH
SPECTRAL PARAMETER

A.B. Amanzholova$^1$, N.S. Imanbaev$^2$, A.D. Niyazymbetov$^3$
$^{1,2}$Department of Mathematics
Akhmet Yasawi International Kazakh-Turkish University
29, Sattarkhanov Street, 161200 Turkistan, KAZAKHSTAN
$^2$South Kazakhstan State Pedagogical Institute
Shymkent, KAZAKHSTAN


Abstract. In this paper we consider the spectral problem for the Cauchy-Riemann operator with Bicadze - Samarskii type boundary value conditions, reduced to a singular integral equation with continuous kernel. Moreover, we characterize those spectral parameters at which the inhomogeneous boundary value problem with shift into the region for Cauchy-Riemann equations is everywhere solvable in the class of continuous functions on the unit circle.

Received: March 3, 2014

AMS Subject Classification: 32W50, 65N35

Key Words and Phrases: Cauchy-Riemann operator, space of continuous functions, Fredholm, resolvent set, resolvent, problem with shift into the region, kernel

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DOI: 10.12732/ijpam.v93i3.13 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 3
Pages: 449 - 461

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).