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Results Math (2024) 79:66
c
2024 The Author(s), under exclusive licence to
Springer Nature Switzerland AG
1422-6383/24/020001-22
published online January 13, 2024
https://doi.org/10.1007/s00025-023-02092-1 Results in Mathematics
Approximation by Multivariate
Max-Product Kantorovich Exponential
Sampling Operators
Sathish Kumar Angamuthu
Abstract. The approximation behavior of multivariate max-product Kan-
torovich exponential sampling operators has been analyzed. The point-
wise and uniform approximation theorem for these sampling series Iχ,(M)
w,j
is proved. The degree of approximation in-terms of logarithmic modulus
of smoothness is studied. For the class of log-H¨olderian functions, the
order of uniform norm convergence is established. The norm-convergence
theorems for the multivariate max-product Kantorovich exponential sam-
pling operators in Mellin–Lebesgue spaces is studied.
Mathematics Subject Classification. 41A35, 94A20, 41A25.
Keywords. Multivariate max-product operators, Kantorovich sampling
operators, degree of approximation, Mellin–Lebesgue spaces.
1. Introduction
One of the fundamental results in Fourier analysis is the celebrated Shannon
sampling theorem due to Wittaker, Kotelnikov and Shannon (see [29]). The
sampling theorem has played an important role in the areas of approximation
theory, harmonic analysis, signal and image processing etc., due to the fact
that it provides a tool to convert analog signals into a discrete sequence of
samples without loosing the actual information.Though WKS sampling theo-
rem is one of the most influential result in the theory of approximation but
certainly it requires strong assumptions on the functions to be approximated.
Butzer and Stens [19] initiated the study of generalized sampling series for
not necessarily band limited signals. They have replaced the sinc-function in
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