Choose an application

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

This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.

Functional analysis --- Harmonic analysis. Fourier analysis --- Partial differential equations --- Differential equations --- Fourieranalyse --- differentiaalvergelijkingen --- functies (wiskunde)

Choose an application

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

Questo libro trae la sua origine dagli appunti preparati per le lezioni di Metodi Matematici della Fisica tenute al Dipartimento di Fisica dell'Università di Pisa, e via via sistemati, raffinati e aggiornati nel corso di molti anni di insegnamento. L'intento generale è di fornire una presentazione per quanto possibile semplice e diretta dei metodi matematici basilari e rilevanti per la Fisica. Anche allo scopo di mantenere questo testo entro i limiti di un manuale di dimensioni contenute e di agevole consultazione, sono stati spesso sacrificati i dettagli tecnici delle dimostrazioni matematiche (o anzi le dimostrazioni per intero) e anche i formalismi eccessivi, che tendono a nascondere la vera natura dei problemi. Al contrario, si è cercato di evidenziare – per quanto possibile – le idee sottostanti e le motivazioni che conducono ai diversi procedimenti. L'obiettivo principale e quello di mettere in condizione chi ha letto questo libro di acquisire gli strumenti adatti e le conoscenze di base che gli permettano di affrontare senza difficoltà anche testi più avanzati e impegnativi. Questa nuova Edizione conserva la struttura generale della prima Edizione, ma è arricchita dall'inserimento di numerosi esempi (e controesempi), con nuove osservazioni e chiarimenti su tutti gli argomenti proposti: Serie di Fourier, Spazi di Hilbert, Operatori lineari, Funzioni di Variabile complessa, Trasformate di Fourier e di Laplace, Distribuzioni. Inoltre, le prime nozioni della Teoria dei Gruppi, delle Algebre di Lie e delle Simmetrie in Fisica (che erano confinate in una Appendice nella Prima Edizione) vengono ora proposte in una forma sensibilmente ampliata, con vari esempi in vista delle applicazioni alla Fisica. In particolare, due nuovi Capitoli sono dedicati allo studio delle proprietà di simmetria dell'atomo di idrogeno e dell'oscillatore armonico in Meccanica Quantistica.

Group theory --- Algebraic geometry --- Functional analysis --- Harmonic analysis. Fourier analysis --- Mathematical physics --- Physics --- Fourieranalyse --- complexe veranderlijken --- functies (wiskunde) --- wiskunde --- fysica

Choose an application

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

This book discusses recent developments in and the latest research on mathematics, statistics and their applications. All contributing authors are eminent academics, scientists, researchers and scholars in their respective fields, hailing from around the world. The book presents roughly 60 unpublished, high-quality and peer-reviewed research papers that cover a broad range of areas including approximation theory, harmonic analysis, operator theory, fixed-point theory, functional differential equations, dynamical and control systems, complex analysis, special functions, function spaces, summability theory, Fourier and wavelet analysis, and numerical analysis – all of which are topics of great interest to the research community – while further papers highlight important applications of mathematical analysis in science, engineering and related areas. This conference aims at bringing together experts and young researchers in mathematics from all over the world to discuss the latest advances in mathematical analysis, and at promoting the exchange of ideas in various applications of mathematics in engineering, physics and biology. This conference encourages international collaboration and provides young researchers an opportunity to learn about the current state of the research in their respective fields.

Algebraic geometry --- Operator theory --- Harmonic analysis. Fourier analysis --- Mathematical analysis --- Mathematics --- Computer. Automation --- Fourieranalyse --- analyse (wiskunde) --- complexe veranderlijken --- reeksen (wiskunde) --- Fourierreeksen --- computers --- informatica --- mathematische modellen --- wiskunde

Choose an application

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

The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications. .

Differential geometry. Global analysis --- Functional analysis --- Harmonic analysis. Fourier analysis --- Partial differential equations --- Differential equations --- Numerical methods of optimisation --- Mathematics --- Fourieranalyse --- differentiaalvergelijkingen --- analyse (wiskunde) --- Laplacetransformatie --- differentiaal geometrie --- functies (wiskunde) --- wiskunde --- kansrekening --- optimalisatie

Choose an application

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

The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations.

Harmonic analysis. Fourier analysis --- Partial differential equations --- Operational research. Game theory --- Discrete mathematics --- Mathematical statistics --- Probability theory --- Mathematics --- Classical mechanics. Field theory --- Statistical physics --- Fourieranalyse --- differentiaalvergelijkingen --- waarschijnlijkheidstheorie --- grafentheorie --- stochastische analyse --- statistiek --- fysica --- kansrekening --- dynamica