Carlo Bardaro – författare
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2 produkter
2 produkter
Mellin Analysis, Transform Theory, and Applications
A Self-Contained Approach
Inbunden, Engelska, 2026
1 704 kr
Skickas inom 10-15 vardagar
This monograph presents the theory of the Mellin transform and the resulting Mellin analysis in a rigorous and unified manner. Often dismissed as a subordinate topic within Fourier and Laplace transform, it is instead demonstrated here that the theory is completely independent, can be studied within a self-contained framework, and exhibits some typical characteristics.In addition to highlighting the foundations of the theory, the book addresses applications to certain partial differential equations, sampling theory and numerical quadrature. These applications provide methods which are in turn of interest in various areas of mathematics, science, and engineering.Each chapter is enriched by numerous references to further literature and potential research directions. Researchers working in this field will gain new insights and appreciate the deserved attention for this underrated topic in harmonic analysis.
2 533 kr
Skickas inom 5-8 vardagar
In 1903 Fredholm published his famous paper on integral equations. Since then linear integral operators have become an important tool in many areas, including the theory of Fourier series and Fourier integrals, approximation theory and summability theory, and the theory of integral and differential equations. As regards the latter, applications were soon extended beyond linear operators. In approximation theory, however, applications were limited to linear operators mainly by the fact that the notion of singularity of an integral operator was closely connected with its linearity.This book represents the first attempt at a comprehensive treatment of approximation theory by means of nonlinear integral operators in function spaces. In particular, the fundamental notions of approximate identity for kernels of nonlinear operators and a general concept of modulus of continuity are developed in order to obtain consistent approximation results. Applications to nonlinear summability, nonlinear integral equations and nonlinear sampling theory are given. In particular, the study of nonlinear sampling operators is important since the results permit the reconstruction of several classes of signals.In a wider context, the material of this book represents a starting point for new areas of research in nonlinear analysis. For this reason the text is written in a style accessible not only to researchers but to advanced students as well.