Harmonic Analysis, Partial Differential Equations, Banach Spaces, and Operator Theory (Volume 2)


Book Description

This book is the second of a two volume series. Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book features fully-refereed, high-quality papers exploring new results and trends in weighted norm inequalities, Schur-Agler class functions, complex analysis, dynamical systems, and dyadic harmonic analysis. Graduate students and researchers in analysis will find inspiration in the articles collected in this volume, which emphasize the remarkable connections between harmonic analysis and operator theory. A survey of the two weight problem for the Hilbert transform and an expository article on the Clark model to the case of non-singular measures and applications to the study of rank-one perturbations are included. The material for this volume is based on the 13th New Mexico Analysis Seminar held at the University of New Mexico, April 3-4, 2014 and on several special sections of the Western Spring Sectional Meeting at the University of New Mexico, April 4-6,2014. During the event, participants honored the memory of Cora Sadosky—a great mathematician who recently passed away and who made significant contributions to the field of harmonic analysis. Cora was an exceptional scientist and human being. She was a world expert in harmonic analysis and operator theory, publishing over fifty-five research papers and authoring a major textbook in the field. Participants of the conference include new and senior researchers, recent doctorates as well as leading experts in the area.




New Trends in Applied Harmonic Analysis, Volume 2


Book Description

This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. 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. 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. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.




Fuzzy Systems and Data Mining VI


Book Description

The interdisciplinary field of fuzzy logic encompass applications in the electrical, industrial, chemical and engineering realms as well as in areas of management and environmental issues, while data mining covers new approaches to big data, massive data, and scalable, parallel and distributed algorithms. This book presents papers from the 6th International Conference on Fuzzy Systems and Data Mining (FSDM 2020). The conference was originally due to be held from 13-16 November 2020 in Xiamen, China, but was changed to an online conference held on the same dates due to ongoing restrictions connected with the COVID-19 pandemic. The annual FSDM conference provides a platform for knowledge exchange between international experts, researchers academics and delegates from industry. This year, the committee received 316 submissions, of which 76 papers were selected for inclusion in the conference; an acceptance rate of 24%. The conference covers four main areas: fuzzy theory; algorithms and systems, which includes topics like stability; foundations and control; and fuzzy applications, which are widely used and cover various types of processing as well as hardware and architecture for big data and time series. Providing a current overview of research and developments in fuzzy logic and data mining, the book will be of interest to all those working in the field of data science.




Pediatric Orthopedic Deformities, Volume 2


Book Description

Volume 2 of this comprehensive and state-of-the-art text on pediatric orthopedic deformities focuses on conditions of the lower extremity. Developmental disorders of the hip – developmental dysplasia of the hip (DDH), Legg-Calvé-Perthes disease (LCP), coxa vara including slipped capital femoral epiphysis (SCFE), and femoroacetabular impingement (FAI) – the knee, the ankle and foot, as well as rotational and angular deformities of the lower limb are discussed in detail. Presentation for each deformity includes: definition, detailed review of the pathoanatomy, experimental biological investigations (where applicable), natural history, review of the evolution of diagnostic and treatment techniques, results achieved with the various approaches, and current management approaches with detailed descriptions of surgical technique. Extensive illustrations, figures and photos provide clear visual depictions of the range of deformity for the various disorders, underlying histopathology, imaging findings and treatment approaches. Multiple tables provide concentrated information, especially for the treatment options based on the severity of the particular disorder and deformity. Based on a solid understanding of the underlying pathobiology of deformities of the developing musculoskeletal system, this second volume of Pediatric Orthopedic Deformities provides a penetrating, in-depth presentation on the lower extremity for pediatric orthopedic surgeons, adult orthopedic surgeons seeking a deeper understanding of how deformities developed, and all clinicians caring for pediatric patients with developmental deformities.




Topics in Operator Theory


Book Description

This is the second volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.




Operator Theory in Function Spaces


Book Description

This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.




Operator Methods in Ordinary and Partial Differential Equations


Book Description

CO«i»b.H BaCHJIbeBHa lU>BaJIeBcR8JI (Sonja Kovalevsky) was born in Moscow in 1850 and died in Stockholm in 1891. Between these years, in the then changing and turbulent circumstances for Europe, lies the all too brief life of this remarkable woman. This life was lived out within the great European centers of power and learning in Russia, France, Germany, Switzerland, England and Sweden. To this day, now 150 years after her birth, her influence for and contribution to mathe matics, science, literature, women's rights and democratic government are recorded and reviewed, not only in Europe but now in countries far removed in time and distance from the lands of her birth and being. This volume, dedicated to her memory and to her achievements, records the Proceedings of the Marcus Wallenberg Symposium held, in memory of Sonja Kovalevsky, at Stockholm University from 18 to 22 June 2000. The symposium was held at the Department of Mathematics with its excellent library and lecture halls providing favourable working conditions. Within these pages are contained a curriculum vitae for Sonja Kovalevsky, a list of all her scientific publications, together with a copy of the moving and elegant obituary notice written by her friend and protector Gosta Mittag-Leffler. These papers are followed by a leading article entitled Sonja Kovalevsky: Her life and professorship in Stockholm, written especially for this volume by Jan-Erik Bjork in preparation for his major address to the Symposium.




Hilbert Transforms: Volume 2


Book Description

The definitive reference on Hilbert transforms covering the mathematical techniques for evaluating them, and their application.




Advanced R


Book Description

An Essential Reference for Intermediate and Advanced R Programmers Advanced R presents useful tools and techniques for attacking many types of R programming problems, helping you avoid mistakes and dead ends. With more than ten years of experience programming in R, the author illustrates the elegance, beauty, and flexibility at the heart of R. The book develops the necessary skills to produce quality code that can be used in a variety of circumstances. You will learn: The fundamentals of R, including standard data types and functions Functional programming as a useful framework for solving wide classes of problems The positives and negatives of metaprogramming How to write fast, memory-efficient code This book not only helps current R users become R programmers but also shows existing programmers what’s special about R. Intermediate R programmers can dive deeper into R and learn new strategies for solving diverse problems while programmers from other languages can learn the details of R and understand why R works the way it does.




Convergence and Summability of Fourier Transforms and Hardy Spaces


Book Description

This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations. Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike.