Volume 1 covered foundational topics such as distributional and fractional calculus, the integral transform, and wavelets, and Volume 2 explored linear and nonlinear dynamics in continuous media. The needs of the applied-sciences audience are addressed by a careful and rich selection of examples arising in real-life industrial and scientific labs and a thorough discussion of their physical significance.

The topics included are Fourier analysis, Padè approximation, dynamical systems and difference operators, splines, Christoffel functions, best approximation, discrepancy theory and Jackson-type theorems of approximation..The articles of this collection were originated from the International Conference in Approximation Theory, held in Savannah, GA in 2017, and organized by the editors of this volume. Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume.

The topics included are Fourier analysis, Padè approximation, dynamical systems and difference operators, splines, Christoffel functions, best approximation, discrepancy theory and Jackson-type theorems of approximation..The articles of this collection were originated from the International Conference in Approximation Theory, held in Savannah, GA in 2017, and organized by the editors of this volume. Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume.

Metrics, Norms, Inner Products, and Operator Theory Written in an appealing and accessible style, Metrics, Norms, Inner Products, and Operator Theory is suitable for independent study or as the basis for an undergraduate-level course.com/978-3-319-65321-1). Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory. Extensive exercises complement the text and provide opportunities for learning by doing.

This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform. The XFT Quadrature in Discrete Fourier Analysis.

This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform. The XFT Quadrature in Discrete Fourier Analysis.

Counting Lattice Paths Using Fourier Methods is ideal for upper-undergraduates and graduate students studying combinatorics or other areas of mathematics, as well as computer science or physics.

Counting Lattice Paths Using Fourier Methods is ideal for upper-undergraduates and graduate students studying combinatorics or other areas of mathematics, as well as computer science or physics.Counting Lattice Paths Using Fourier Methods This monograph introduces a novel and effective approach to counting lattice paths by using the discrete Fourier transform (DFT) as a type of periodic generating function..

These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing.

This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform. The XFT Quadrature in Discrete Fourier Analysis.

These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing.

These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems.New Trends in Applied Harmonic Analysis, Volume 2 Some topics covered include: Gabor frames Falconer distance problem Hausdorff dimension Sparse inequalities Fractional Brownian motion Fourier analysis in geometric measure theory This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing.

Recent Advances in Mathematics and Technology.There is a particular emphasis on stochastic analysis, machine learning algorithms, and deep learning models, which are highly relevant to the state-of-the-art in augmented, virtual, and mixed realities. Advances in mathematical modeling, optimization, numerical analysis, signal processing, and computer science are presented by leading experts in these fields.

Recent Advances in Mathematics and Technology.There is a particular emphasis on stochastic analysis, machine learning algorithms, and deep learning models, which are highly relevant to the state-of-the-art in augmented, virtual, and mixed realities. Advances in mathematical modeling, optimization, numerical analysis, signal processing, and computer science are presented by leading experts in these fields. The chapters in this volume are based on talks given at the inaugural Technology, Engineering and Mathematics Conference (TEM18), held from March 26 to 27, 2018 in Kenitra, Morocco.

Modulation Spaces.Because it is almost entirely self-contained, these insights will be accessible to a wide audience of interested readers. Modulation Spaces will be an ideal reference for researchers in time-frequency analysis and nonlinear partial differential equations. This monograph serves as a much-needed, self-contained reference on the topic of modulation spaces.

Recent Advances in Mathematics and Technology.There is a particular emphasis on stochastic analysis, machine learning algorithms, and deep learning models, which are highly relevant to the state-of-the-art in augmented, virtual, and mixed realities. Advances in mathematical modeling, optimization, numerical analysis, signal processing, and computer science are presented by leading experts in these fields. The chapters in this volume are based on talks given at the inaugural Technology, Engineering and Mathematics Conference (TEM18), held from March 26 to 27, 2018 in Kenitra, Morocco.

The focus then expands to the many valuable applications of modulation spaces, such as linear and multilinear pseudodifferential operators, and dispersive partial differential equations. Foundational concepts and definitions in functional, harmonic, and real analysis are reviewed in the first chapter, which is then followed by introducing modulation spaces. This monograph serves as a much-needed, self-contained reference on the topic of modulation spaces.

The papers highlight state-of-the-art advances and trends in sampling theory and related areas of application, such as signal and image processing.

.The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University.

The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday.

The papers highlight state-of-the-art advances and trends in sampling theory and related areas of application, such as signal and image processing.

The papers highlight state-of-the-art advances and trends in sampling theory and related areas of application, such as signal and image processing.Sampling: Theory and Applications Claude Shannon’s 100th birthday is also celebrated, including an introductory essay that highlights Shannon’s profound influence on the field. Chapters have been written by prominent mathematicians, applied scientists, and engineers with an expertise in sampling theory.

The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University. The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday.. The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018.

Foundational concepts and definitions in functional, harmonic, and real analysis are reviewed in the first chapter, which is then followed by introducing modulation spaces. This monograph serves as a much-needed, self-contained reference on the topic of modulation spaces. Modulation Spaces will be an ideal reference for researchers in time-frequency analysis and nonlinear partial differential equations. It will also appeal to graduate students and seasoned researchers who seek an introduction to the time-frequency analysis of nonlinear dispersive partial differential equations.

This book provides an introduction to discrete harmonic analysis (DHA) with a view towards applications to digital signal processing.With only modest prerequisites, some of which are recalled at the beginning, a profound mathematical theory is built almost from scratch.

Based decades of teaching experience, this book provides a basis for lecture courses starting at the upper undergraduate level, and will also prove a valuable resource for mathematicians and engineers interested in digital signal processing. Fast algorithms are used to process signals in real time, while additional options are provided by spline harmonic analysis. Foundations of Discrete Harmonic Analysis.

Landscapes of Time-Frequency Analysis.New results are collected as well, making this a valuable resource for readers seeking to be brought up-to-date. Written by experts in harmonic analysis and its applications, these chapters provide a valuable overview of the state-of-the-art of this active area of research.

Also included are the introduction to his PhD thesis and an unpublished paper coauthored by him. This edited volume features chapters written by some of these colleagues, as well as researchers whom Grossmann’s work and way of thinking has impacted in a decisive way. Theoretical Physics, Wavelets, Analysis, Genomics His lasting influence can be seen not only in his research and numerous publications, but also through the relationships he cultivated with his collaborators and students..

. Theoretical Physics, Wavelets, Analysis, Genomics His lasting influence can be seen not only in his research and numerous publications, but also through the relationships he cultivated with his collaborators and students. Also included are the introduction to his PhD thesis and an unpublished paper coauthored by him.

New results are collected as well, making this a valuable resource for readers seeking to be brought up-to-date. This contributed volume features chapters based on talks given at the second international conference titled Aspects of Time-Frequency Analysis (ATFA 19), held at Politecnico di Torino from June 25th to June 27th, 2019. Landscapes of Time-Frequency Analysis. Written by experts in harmonic analysis and its applications, these chapters provide a valuable overview of the state-of-the-art of this active area of research.