Integral calculus and equations

Operator Functions and Localization of Spectra is the first book that presents a systematic exposition of bounds for the spectra of various linear nonself-adjoint operators in a Hilbert space, having discrete and continuous spectra.

The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent.

This book presents the foundations of the inverse scattering method and its applications to the theory of solitons in such a form as we understand it in Leningrad.

Based on a graduate course given by the author at Yale University this book deals with complex analysis (analytic capacity), geometric measure theory (rectifiable and uniformly rectifiable sets) and harmonic analysis (boundedness of singular integral operators on Ahlfors-regular sets).

Many of problems of the natural sciences lead to nonlinear partial differential equations.

This book consists of six survey contributions that are focused on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids.

This proceedings volume convenes works within the field of fractional calculus and its applications, presented at the International Conference on Fractional Differentiation and its Applications (ICFCA), held in Sousse, Tunisia, from December 26th to 30th, 2024.

This proceedings volume convenes works within the field of fractional calculus and its applications, presented at the International Conference on Fractional Differentiation and its Applications (ICFCA), held in Sousse, Tunisia, from December 26th to 30th, 2024.

This book can serve as a first course on measure theory and measure theoretic probability for upper undergraduate and graduate students of mathematics, statistics and probability.

This volume presents the extended abstracts from the 2024 Summer School organized by the Ghent Analysis and PDE Center.

This volume presents the extended abstracts from the 2024 Summer School organized by the Ghent Analysis and PDE Center.

This book provides a new approach to traces, which are viewed as linear continuous functionals on some function space.

This book provides a new approach to traces, which are viewed as linear continuous functionals on some function space.

This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields.

Integration is the sixth and last of the Books that form the core of the Bourbaki series; it draws abundantly on the preceding five Books, especially General Topology and  Topological Vector Spaces, making it a culmination of the core six.

This book presents the theory of Bessel wavelet transformation involving Hankel transformation.

This book presents the theory of Bessel wavelet transformation involving Hankel transformation.

This book presents a concise introduction to real and complex number systems and metric space theory.

This book presents a concise introduction to real and complex number systems and metric space theory.

Inverse problems lie at the core of scientific discovery, enabling us to determine causes from observed consequences.

This textbook offers an introduction to ODEs that focuses on the qualitative behavior of differential equations rather than specialized methods for solving them.

This textbook offers an introduction to ODEs that focuses on the qualitative behavior of differential equations rather than specialized methods for solving them.

Targeted to upper-undergraduate and graduate students of mathematics, this book discusses special integrals and their applications in finding certain series sums.

Targeted to upper-undergraduate and graduate students of mathematics, this book discusses special integrals and their applications in finding certain series sums.

This self-contained book offers an extensive state-of-the-art exposition of rotational integral geometry, a field that has reached significant maturity over the past four decades.

This self-contained book offers an extensive state-of-the-art exposition of rotational integral geometry, a field that has reached significant maturity over the past four decades.

This monograph presents the work of the authors in metrical theory of continued fractions in the last two decades.

This book highlights the mathematical, physical, and technical properties of moving acoustic sources.

This book highlights the mathematical, physical, and technical properties of moving acoustic sources.

This monograph presents the work of the authors in metrical theory of continued fractions in the last two decades.

This volume contains the contributions of the participants of the 14th ISAAC congress, held at the University of Sao Paulo, Campus Ribeirao Preto, Brazil, on July 17-21, 2023.

The flourishing theory of classical optimal transport concerns mass transportation at minimal cost.

The flourishing theory of classical optimal transport concerns mass transportation at minimal cost.

Unlock the intricate language of signals and systems with this in-depth exploration of Fourier and Laplace transforms.

This book compiles an extensive list of solved and proposed problems in mathematical topics in analysis, aimed at students of mathematics, applied mathematics, physics, and engineering.

This book compiles an extensive list of solved and proposed problems in mathematical topics in analysis, aimed at students of mathematics, applied mathematics, physics, and engineering.

Designed for senior undergraduate and graduate students in mathematics, this textbook offers a comprehensive exploration of measure theory and integration.

This monograph delves into the theory of time-fractional diffusion and wave equations, presenting a comprehensive exploration of recent advancements in the field.

This monograph delves into the theory of time-fractional diffusion and wave equations, presenting a comprehensive exploration of recent advancements in the field.

The aim of this volume is to present some new developments and ideas in partial differential equations and mathematical analysis, including spectral analysis and boundary value problems for PDE, harmonic analysis, inequalities, integral equations, and applications.

The aim of this volume is to present some new developments and ideas in partial differential equations and mathematical analysis, including spectral analysis and boundary value problems for PDE, harmonic analysis, inequalities, integral equations, and applications.

This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport.

This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport.

This book aims to present some recent results on Prandtl equations and MHD boundary layer equations.

This book aims to present some recent results on Prandtl equations and MHD boundary layer equations.

This textbook proposes an informal access to the most important issues of multidimensional differential and integral calculus.

This textbook proposes an informal access to the most important issues of multidimensional differential and integral calculus.

This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century.