Presents a new quadrature formula for the fractional Fourier transform
Many examples are addressed to illustrate the power of the new formula
Most of the algorithms presented, are implemented in standard packages as
MATLAB or MATHEMATICA
Present the XFT matrix as a finite-dimensional transformation
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. In turn, the book’s second goal is to present the XFT matrix as a
finite-dimensional transformation that links certain discrete operators in the same way that the
corresponding continuous operators are related by the Fourier transform, and to show that the
XFT matrix accordingly generates sequences of matrix operators that represent continuum
operators, and which allow these operators to be studied from another perspective.
1st ed. 2019, XIII, 235 p.
100 illus., 96 illus. in color.
Hardcover
ISBN 978-3-030-13422-8
Softcover
ISBN 978-3-030-13425-9
Product category : Monograph
Series : Applied and Numerical Harmonic Analysis
Mathematics : Special Functions
Includes a new chapter that provides an in-depth exploration of CauchyRiemann geometry
Uses the concept of orthogonality to unify various mathematical topics
Includes accessible content designed to lead students from undergraduate to research-level mathematics
This textbook provides a coherent, integrated look at various topics from undergraduate
analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier
transform on the real line, and then turns to the heart of the book, geometric considerations.
This chapter includes complex differential forms, geometric inequalities from one and several
complex variables, and includes some of the author's original results. The concept of
orthogonality weaves the material into a coherent whole. This textbook will be a useful
resource for upper-undergraduate students who intend to continue with mathematics, graduate
students interested in analysis, and researchers interested in some basic aspects of CauchyRiemann (CR) geometry.
The inclusion of several hundred exercises makes this book suitable
for a capstone undergraduate Honors class. This second edition contains a significant amount
of new material, including a new chapter dedicated to the CR geometry of the unit sphere. This
chapter builds upon the first edition by presenting recent results about groups associated with
CR sphere maps. From reviews of the first edition: The present book developed from the
teaching experiences of the author in several honors courses. …. All the topics are motivated
very nicely, and there are many exercises, which make the book ideal for a first-year graduate
course on the subject. …. The style is concise, always very neat, and proofs are given with full
details. Hence, I certainly suggest this nice textbook to anyone interested in the subject, even
for self-study. Fabio Nicola, Politecnico di Torino, Mathematical Reviews D’Angelo has written an
eminently readable book, including excellent explanations of pretty nasty stuff for even the
more gifted upper division players .... It certainly succeeds in hooking the present browser: I
like this book a great deal. Michael Berg, Loyola Marymount University, Mathematical
Association of America
2nd ed. 2019, X, 229 p. 28 illus., 20 illus. in color.
Hardcover
ISBN 978-3-030-16513-0
Softcover
ISBN 978-3-030-16516-1
Product category : Graduate/advanced undergraduate textbook
Series : Cornerstones
Other renditions
Softcover
ISBN 978-3-030-16516-1
Mathematics : Functions of a Complex Variable
Covers topics from applied mathematics, physics and engineering
Addresses the development, mathematical analysis, and application of
meshfree and particle methods especially to multiscale phenomena
This volume collects selected papers presented at the Ninth International Workshop on
Meshfree Methods held in Bonn, Germany in September 2017. They address various aspects of
this very active research field and cover topics from applied mathematics, physics and
engineering. The numerical treatment of partial differential equations with meshfree
discretization techniques has been a very active research area in recent years. While the
fundamental theory of meshfree methods has been developed and considerable advances of
the various methods have been made, many challenges in the mathematical analysis and
practical implementation of meshfree methods remain. This symposium aims to promote
collaboration among engineers, mathematicians, and computer scientists and industrial
researchers to address the development, mathematical analysis, and application of meshfree
and particle methods especially to multiscale phenomena. It continues the 2-year-cycled
Workshops on Meshfree Methods for Partial Differential Equations.
1st ed. 2019, VIII, 206 p.
64 illus., 30 illus. in color.
Hardcover
ISBN 978-3-030-15118-8
Softcover
ISBN 978-3-030-15121-8
Product category : Contributed volume
Series : Lecture Notes in Computational Science and Engineering
Mathematics : Numerical Analysis
Presents a collection of Professor Kripa Shankar Shukla’ papers highlighting
the wide range of his scholarship
Consists revised articles of the third unpublished part of “History of Hindu
Mathematics” by Bibhutibhusan Datta and Avadhesh Narayan Singh
Includes some of Professor Shukla’s reviews of works related to Indian
mathematics and astronomy authored by various scholars
This volume presents a collection of some of the seminal articles of Professor K. S. Shukla who
made immense contributions to our understanding of the history and development of
mathematics and astronomy in India. It consists of six parts: Part I constitutes introductory
articles which give an overview of the life and work of Prof. Shukla, including details of his
publications, reminiscences from his former students, and an analysis of his monumental
contributions. Part II is a collection of important articles penned by Prof. Shukla related to
various aspects of Indian mathematics. Part III consists of articles by Bibhutibhusan Datta and
Avadhesh Narayan Singh—which together constitute the third unpublished part of their History
of Hindu Mathematics—that were revised and updated by Prof. Shukla. Parts IV and V consist
of a number of important articles of Prof. Shukla on different aspects of Indian astronomy.
Part VI includes some important reviews authored by him and a few reviews of his work. Given
the sheer range and depth of Prof. Shukla’s scholarship, this volume is essential reading for
scholars seeking to deepen their understanding of the rich and varied contributions made by
Indian mathematicians and astronomers
1st ed. 2019, XXII, 742 p. 2 illus.
Hardcover
ISBN 978-981-13-7325-1
Softcover
ISBN 978-981-13-7328-2
Product category : Contributed volume
Series : Sources and Studies in the History of Mathematics and Physical Sciences
Mathematics : History of Mathematics
Collects over 240 solved examples and counterexamples with applications
Includes numerous end-of-chapter comprehension problems
Presents a lucid exposition of proofs of theorems
Includes a solutions manual for instructors
Topology is a large subject with several branches, broadly categorized as algebraic topology,
point-set topology, and geometric topology. Point-set topology is the main language for a
broad range of mathematical disciplines, while algebraic topology offers as a powerful tool for
studying problems in geometry and numerous other areas of mathematics. This book presents
the basic concepts of topology, including virtually all of the traditional topics in point-set
topology, as well as elementary topics in algebraic topology such as fundamental groups and
covering spaces. It also discusses topological groups and transformation groups. When
combined with a working knowledge of analysis and algebra, this book offers a valuable
resource for advanced undergraduate and beginning graduate students of mathematics
specializing in algebraic topology and harmonic analysis
1st ed. 2019, XIX, 452 p. 93 illus.
Hardcover
ISBN 978-981-13-6953-7
Softcover
ISBN 978-981-13-6956-8
Product category : Graduate/advanced undergraduate textbook
Mathematics : Topology
Explores Gallai-Ramsey Theory
Contains strategies and technique to obtain fundamental results
Features complete proofs, open problems, and detailed illustrations
This book explores topics in Gallai-Ramsey theory, which looks into whether rainbow colored
subgraphs or monochromatic subgraphs exist in a sufficiently large edge-colored complete
graphs. A comprehensive survey of all known results with complete references is provided for
common proof methods. Fundamental definitions and preliminary results with illustrations
guide readers to comprehend recent innovations. Complete proofs and influential results are
discussed with numerous open problems and conjectures. Researchers and students with an
interest in edge-coloring, Ramsey Theory, and colored subgraphs will find this book a valuable
guide for entering Gallai-Ramsey Theory
1st ed. 2020, VIII, 104 p. 67 illus.
Softcover
ISBN 978-3-030-48896-3
Product category : Brief
Series : SpringerBriefs in Mathematics
Mathematics : Graph Theory