This work covers two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated.

This volume concentrates on how to construct a Markov process by starting with a suitable pseudo-differential operator. Feller processes, Hunt processes associated with Lp-sub-Markovian semigroups and processes constructed by using the Martingale problem are at the center of the considerations. The potential theory of these processes is further developed and applications are discussed. Due to the non-locality of the generators, the processes are jump processes and their relations to Levy processes are investigated. Special emphasis is given to the symbol of a process, a notion which generalizes that of the characteristic exponent of a Levy process and provides a natural link to pseudo-differential operator theory.

In this volume two topics are discussed: the construction of Feller and Lp-sub-Markovian semigroups by starting with a pseudo-differential operator, and the potential theory of these semigroups and their generators. The first part of the text essentially discusses the analysis of pseudo-differential operators with negative definite symbols and develops a symbolic calculus; in addition, it deals with special approaches, such as subordination in the sense of Bochner. The second part handles capacities, function spaces associated with continuous negative definite functions, Lp -sub-Markovian semigroups in their associated Bessel potential spaces, Stein's Littlewood-Paley theory, global properties of Lp-sub-Markovian semigroups, and estimates for transition functions.

This work covers two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated.

After recalling essentials of analysis OCo including functional analysis, convexity, distribution theory and interpolation theory OCo this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students. Sample Chapter(s). Introduction: Pseudo Differential Operators and Markov Processes (207 KB). Chapter 1: Introduction (190 KB). Contents: Essentials from Analysis: Calculus Results; Convexity; Some Interpolation Theory; Fourier Analysis and Convolution Semigroups: The PaleyOCoWienerOCoSchwartz Theorem; Bounded Borel Measures and Positive Definite Functions; Convolution Semigroups and Negative Definite Functions; The L(r)vyOCoKhinchin Formula for Continuous Negative Definite Functions; Bernstein Functions and Subordination of Convolution Semigroups; Fourier Multiplier Theorems; One Parameter Semigroups: Strongly Continuous Operator Semigroups; Subordination in the Sense of Bochner for Operator Semigroups; Generators of Feller Semigroups; Dirichlet Forms and Generators of Sub-Markovian Semigroups; and other papers. Readership: Graduate students, researchers and lecturers in analysis & differential equations, stochastics, probability & statistics, and mathematical physics."

This volume concentrates on how to construct a Markov process by starting with a suitable pseudo-differential operator. Feller processes, Hunt processes associated with Lp-sub-Markovian semigroups and processes constructed by using the Martingale problem are at the center of the considerations. The potential theory of these processes is further developed and applications are discussed. Due to the non-locality of the generators, the processes are jump processes and their relations to Levy processes are investigated. Special emphasis is given to the symbol of a process, a notion which generalizes that of the characteristic exponent of a Levy process and provides a natural link to pseudo-differential operator theory./a

This volume, like its predecessors, is based on the special session on pseudo-differential operators, one of the many special sessions at the 11th ISAAC Congress, held at Linnaeus University in Sweden on August 14-18, 2017. It includes research papers presented at the session and invited papers by experts in fields that involve pseudo-differential operators. The first four chapters focus on the functional analysis of pseudo-differential operators on a spectrum of settings from Z to Rn to compact groups. Chapters 5 and 6 discuss operators on Lie groups and manifolds with edge, while the following two chapters cover topics related to probabilities. The final chapters then address topics in differential equations.

This book is devoted to new classes of parabolic differential and pseudo-differential equations extensively studied in the last decades, such as parabolic systems of a quasi-homogeneous structure, degenerate equations of the Kolmogorov type, pseudo-differential parabolic equations, and fractional diffusion equations. It will appeal to mathematicians interested in new classes of partial differential equations, and physicists specializing in diffusion processes.

This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.

This volume presents a collection of lectures on linear partial differntial equations and semigroups, nonlinear equations, stochastic evolutionary processes, and evolution problems from physics, engineering and mathematical biology. The contributions come from the 6th International Conference on Evolution Equations and Their Applications in Physica