Harmonic Analysis and Applications

NOTE EDITORE

Harmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. In Harmonic Analysis and Applications, the analysis and synthesis of functions in terms of harmonics is presented in such a way as to demonstrate the vitality, power, elegance, usefulness, and the intricacy and simplicity of the subject. This book is about classical harmonic analysis - a textbook suitable for students, and an essay and general reference suitable for mathematicians, physicists, and others who use harmonic analysis.Throughout the book, material is provided for an upper level undergraduate course in harmonic analysis and some of its applications. In addition, the advanced material in Harmonic Analysis and Applications is well-suited for graduate courses. The course is outlined in Prologue I. This course material is excellent, not only for students, but also for scientists, mathematicians, and engineers as a general reference. Chapter 1 covers the Fourier analysis of integrable and square integrable (finite energy) functions on R. Chapter 2 of the text covers distribution theory, emphasizing the theory's useful vantage point for dealing with problems and general concepts from engineering, physics, and mathematics. Chapter 3 deals with Fourier series, including the Fourier analysis of finite and infinite sequences, as well as functions defined on finite intervals. The mathematical presentation, insightful perspectives, and numerous well-chosen examples and exercises in Harmonic Analysis and Applications make this book well worth having in your collection.

SOMMARIO

Prologue I-Course IPrologue II-Fourier Transforms, Fourier Series, and Discrete Fourier TransformsFourier TransformsDefinitions and Formal CalculationsAlgebraic Properties of Fourier TransformsExamplesAnalytic Properties of Fourier TransformsConvolutionApproximate Identities and ExamplesPointwise Inversion of the Fourier TransformPartial Differential EquationsGibbs PhenomenonThe L2(R) Theory ExercisesMeasures and Distribution TheoryApproximate Identities Definition of DistributionsDifferentiation of DistributionsThe Fourier Transform of DistributionsConvolution of DistributionsOperational CalculusMeasure TheoryDefinitions from Probability TheoryWiener's Generalized Harmonic Analysis (GHA)exp{it2}ExercisesFourier SeriesFourier Series - Definitions and ConvergenceHistory of Fourier SeriesIntegration and Differentiation of Fourier SeriesThe L1(T) and L2(T) Theories A(T) and the Wiener Inversion Theorem Maximum Entropy and Spectral EstimationPrediction and Spectral EstimationDiscrete Fourier TransformFast Fourier TransformPeriodization and SamplingExercisesAppendicesA. Real AnalysisB. Functional AnalysisC. Fourier Analysis FormulasD. Contributors to Fourier AnalysisNotationBibliographyIndex

AUTORE

Benedetto, John J.

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9780849378799
• Collana: Studies in Advanced Mathematics
• Dimensioni: 9 x 6 in Ø 1.40 lb
• Formato: Copertina rigida
• Illustration Notes: 1307 equations
• Pagine Arabe: 356