The aim of this paper is to obtain the solution of the operator equation Tx= y for an infinite band matrix T using its finite-dimensional truncations Tnxn= yn. Several verifiable conditions are given to obtain the invertibility of T. An application in connection with a stable set of sampling for functions belonging to a shift-invariant space is discussed along with an illustration. © 2022, Tusi Mathematical Research Group (TMRG).

S H Kulkarni

Department of Mathematics

R. Radha

K. Sarvesh

Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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Journal	Banach Journal of Mathematical Analysis
Publisher	Birkhauser
ISSN	26622033