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This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevant results. They address recent advances in the field, as well as basic semi group and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.
List of contents
1. Discrete Semi groups and Cosine Operators.- 2. Maximal regularity and the method of Fourier Multipliers.- 3. First Order Linear Difference Equations.- 4. First Order Semi linear Difference Equations.- 5. Second Order Linear Difference Equations.- 6. Second Order Semi linear.- 7. Applications.
Summary
This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevant results. They address recent advances in the field, as well as basic semi group and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.
Additional text
From the book reviews:
“This monograph primarily deals with the maximal regularity problem for different classes of difference equations on Banach spaces. … For researchers in this field, this book will serve as an important reference material. It contains many interesting and important applications which would motivate a researcher. It provides a good deal of references on the topic. The presentation of the materials is lucid and systematic which will definitely impress the reader.” (Narahari Parhi, zbMATH 1306.39001, 2015)
Report
From the book reviews:
"This monograph primarily deals with the maximal regularity problem for different classes of difference equations on Banach spaces. ... For researchers in this field, this book will serve as an important reference material. It contains many interesting and important applications which would motivate a researcher. It provides a good deal of references on the topic. The presentation of the materials is lucid and systematic which will definitely impress the reader." (Narahari Parhi, zbMATH 1306.39001, 2015)
