Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Recurrent sequences (Mathematics) --- Recurrence sequences (Mathematics) --- Recurrences (Mathematics) --- Recurring sequences (Mathematics) --- Recursive sequences (Mathematics) --- Sequences (Mathematics) --- Successions (Matemàtica) --- Seqüències (Matemàtica) --- Seqüències numèriques --- Successions numèriques --- Àlgebra --- Matemàtica --- Sèries (Matemàtica) --- Successions espectrals (Matemàtica) --- Sumabilitat --- Sumes exponencials --- Number theory. --- Number study --- Numbers, Theory of --- Algebra

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book discusses all the major topics of complex analysis, beginning with the properties of complex numbers and ending with the proofs of the fundamental principles of conformal mappings. Topics covered in the book include the study of holomorphic and analytic functions, classification of singular points and the Laurent series expansion, theory of residues and their application to evaluation of integrals, systematic study of elementary functions, analysis of conformal mappings and their applications—making this book self-sufficient and the reader independent of any other texts on complex variables. The book is aimed at the advanced undergraduate students of mathematics and engineering, as well as those interested in studying complex analysis with a good working knowledge of advanced calculus. The mathematical level of the exposition corresponds to advanced undergraduate courses of mathematical analysis and first graduate introduction to the discipline. The book contains a large number of problems and exercises, making it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic skills and test the understanding of concepts. Other problems are more theoretically oriented and illustrate intricate points of the theory. Many additional problems are proposed as homework tasks whose level ranges from straightforward, but not overly simple, exercises to problems of considerable difficulty but of comparable interest.

Mathematical analysis. --- Analysis (Mathematics). --- Sequences (Mathematics). --- Analysis. --- Sequences, Series, Summability. --- Mathematical sequences --- Numerical sequences --- Algebra --- Mathematics --- 517.1 Mathematical analysis --- Mathematical analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejér and Cesàro summability, as well as theta-summation, readers will become more familiar with a wide variety of summability methods. Within the theory of higher dimensional summability of Fourier series, the book also provides a much-needed simple proof of Lebesgue’s theorem, filling a gap in the literature. Recent results and real-world applications are highlighted as well, making this a timely resource. The book is structured into four chapters, prioritizing clarity throughout. Chapter One covers basic results from the one-dimensional Fourier series, and offers a clear proof of the Lebesgue theorem. In Chapter Two, convergence and boundedness results for the lq-summability are presented. The restricted and unrestricted rectangular summability are provided in Chapter Three, as well as the sufficient and necessary condition for the norm convergence of the rectangular theta-means. Chapter Four then introduces six types of Lebesgue points for higher dimensional functions. Lebesgue Points and Summability of Higher Dimensional Fourier Series will appeal to researchers working in mathematical analysis, particularly those interested in Fourier and harmonic analysis. Researchers in applied fields will also find this useful.

Fourier analysis. --- Sequences (Mathematics). --- Measure theory. --- Fourier Analysis. --- Sequences, Series, Summability. --- Measure and Integration. --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Mathematical sequences --- Numerical sequences --- Algebra --- Mathematics --- Analysis, Fourier --- Mathematical analysis --- Summability theory. --- Sequences (Mathematics) --- Series --- Sèries de Fourier --- Sumabilitat --- Teoria de sumabilitat --- Sèries (Matemàtica) --- Successions (Matemàtica) --- Integrals de Fourier --- Sèries trigonomètriques --- Anàlisi de Fourier --- Càlcul --- Integrals de Dirichlet