Advances in Operator Theory and Approximation

Applications and Convergence Techniques
Erscheinungsjahr 2026
ISBN: 978-3-032-40166-3
Verlag: Springer

Buch, Englisch, 206 Seiten, Format (B × H): 168 mm x 240 mm

Reihe: Synthesis Lectures on Mathematics & Statistics

This book provides a rigorous examination of modern operator theory focusing on the construction and convergence of linear positive operators in generalized function spaces. In addition, the book explores how to create "mathematical shortcuts" that accurately represent complex, real-world data using simpler, more manageable formulas. By integrating advanced summability methods-such as A-statistical and deferred weighted convergence, the book provides refined techniques for function approximation. From Fourier signal processing to black-box optimization, these chapters contribute to bridging the gap between abstract functional analysis and its applications. Readers will gain a better understanding of modern linear positive operators and advanced summability methods that extend beyond the limitations of classical approximation theory. A versatile toolset for analyzing convergence within complex, generalized function spaces is provided and equips readers to deal with new problems in signal processing, black-box optimization, and modeling.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Jena, Bidu Bhusan

Dutta, Hemen

Paikray, Susanta Kumar

Fachgebiete

• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Signalverarbeitung
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung

Inhaltsverzeichnis

Modified Bernstein-Chlodowsky-Kantorovich-Choquet Operators and Approximation Properties.- New Developments on Boundedness, Convergence, and Absolute Convergence and Summability with Speed.- Generalized Inverses of Toeplitz Operators.- Enhancing Convergence Properties of Stancu-polya Operators.- Discrete Fourier Series with Ant Bee Colony for Enhanced Black-box Optimization.- On Almost Deferred Euler Statistical Convergence.- Approximation Properties of q-Baskakov-Szász-Stancu Operators in Weighted Musielak-Orlicz Spaces.- A New Class of Pólya-Baskakov-Stancu-Kantorovich Operators and Their Approximation Behavior in Musielak-Orlicz Spaces.- Degree Approximation of Signals of Certain Lipschitz Class by the Product of Natarajan-Euler Summability of its Fourier Series.- Approximation Properties of Mellin-Fejer Convolution Operator in Multidimensional Setting via Summability Methods.

Über Autor(innen)

B.B. Jena, Ph.D., is an Assistant Professor in the Department of Mathematics at Sri Sri University, Cuttack, India. Dr. Jena has extensive research experience in the approximation theory of Fourier series, particularly focusing on Lipschitz, Hölder, and Zygmund classes of functions. His research includes work on summability methods, convergence analysis, and error bounds. He has several publications in reputed journals addressing approximation using summability means and has applied analytical methods using MATLAB and C++. His work has also addressed the Gibbs phenomenon and its mitigation using double Fourier series.

Hemen Dutta, Ph.D., is a Professor in the Department of Mathematics at Gauhati University, Guwahati, India. He has published over 200 publications as research articles, proceedings papers, and book chapters and has also authored and edited several books published by leading publishers. He has organized many academic events and served as a speaker in various national and international events. He is on the editorial board of several SCI/SCIE and Scopus indexed journals and is the receipt of several research projects and grants from various funding agencies. His research interests include applied analysis and mathematical modeling.

Susanta Kumar Paikray, Ph.D., is a Professor in the Department of Mathematics at Veer Surendra Sai University of Technology, Burla, India. He has authored more than 100 scientific research articles in peer-reviewed national and international journals, and his current research interests include several areas of pure and applied mathematical sciences including summability theory, Fourier series, approximation theory, functional analysis, statistical convergence, operations research, and inventory optimization.