A THEORY OF MULTIDIMENSIONAL FREDHOLM INTEGRAL EQUATIONS HAVING SEPARABLE KERNELS: SOLVABLE IN A REGION SURROUNDING BY THE HYPERPLANES


By

Hemant Kumar¹ and R. C. Singh Chandel² 

¹Department of Mathematics, D. A-V. Postgraduate College Kanpur, Uttar Pradesh, India-208001 

²Former Head Department of Mathematics, D. V. Postgraduate College Orai, Uttar Pradesh, India-285001 

Email: palhemant2007@rediffmail.com, rc_chandel@yahoo.com 

(Received: February 23, 2024; In format: March 03, 2024; Revised: March 31, 2024; Accepted: April 05, 2024) 


DOI: https://doi.org/10.58250/jnanabha.2024.54121 



Abstract

In this article, we present a theory of multidimensional Fredholm integral equations, having separable kernels, are solvable in a region surrounded by hyperplanes. In derivation of their solutions, we employ the generalized Hilbert-Schmidt theory involving eigenvalues and corresponding normalized eigen functions obtained by separable kernels in a region surrounded by the hyperplanes. Finally, we apply two variables Gegenbauer polynomials and derive a result on the inequality of the solution for the double symmetric Fredholm integral equation. 


2020 Mathematical Sciences Classification: 45B05, 45C05, 33C99. 

Keywords and Phrases: Multidimensional symmetric Fredholm integral equations, hyperplanes, symmetric kernels, normalized eigen functions, two variables Gegenbauer polynomials, inequality. 

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