Download for FREE in 4 easy steps...
You can also read this in Bookboon.com Premium
300+ Business books exclusively in our Premium eReader
- No adverts
- Advanced features
- Personal library
Users who viewed this item also viewed
Partial differential equations and operators - Fundamental solutions and semigroups Part II
An introduction to partial differential equations
Second-order ordinary differential equations - Special functions, Sturm-Liouville theory and transforms
Examples of Differential Equations of Second...
Matrix Methods and Differential Equations - A Practical Introduction
Integration and differential equations
Examples of Systems of Differential Equations...
Hilbert Spaces and Operators on Hilbert Spaces - Functional Analysis Examples c-3
About the book
In this book, which is basically self-contained, we concentrate on partial differential equations in mathematical physics and on operator semigroups with their generators. A central theme is a thorough treatment of distribution theory. This is done via convolution products, Fourier transforms, and fundamental solutions of partial differential operators with constant coefficients. Linear initial value problems are treated via operator semigroups. A relationship between so-called Feller-Dynkin semigroups and Markov processes is described. Finally, Feynman-Kac semigroups are introduced.
- Distributions, differential operators and examples
- Topics to be treated in this book
- Partition of unity
- Test functions and distributions
- Tempered distributions and Fourier transforms
- Examples of Fourier transforms
- Fundamental solutions
- Introduction and examples
- Fundamental solutions of the wave operator
- Fundamental solutions of the wave operator in one space dimension
- Fundamental solutions of the wave equationin several space dimensions
- Proofs of some main results
- Convolution products: formulation of some results
- Fourier transform and its inverse
- Theorem of Malgrange and Ehrenpreis
- Sobolev theory
- Elliptic operators
- 1 Sobolev spaces
- Paley-Wiener theorems
- Multiplicative distributions
- Operators in Hilbert space Part
- Some results in Banach algebras
- Closed linear operators
- Operator semigroups and Markov processes
- Generalities on semigroups
- Markov processes
- Feynman-Kac semigroups Part II
- Harmonic functions on a strip
- Elements of functional analysis
- Theorem of Hahn-Banach
- Banach-Steinhaus theorems: barreled spaces
- Subjects for further research and presentations
To see Section 5–9 download Partial differential equations and operators: Part II
About the Author
Since 2009 the author is retired from the University of Antwerp. Until the present day his teaching duties include a course on ``Partial Differential Equations and Operators’’ and one on ``Advanced Stochastic Processes’’. In the sixties the author was a student at the Catholic University of Nijmegen, Netherlands (nowadays Radboud University), and he earned his Ph.D. from the University of Hawaii, USA, (1971). Since 1972 he has been a member of the academic staff of the University of Antwerp, Department of Mathematics and Computer Science, Belgium. Most of his professional life he has been teaching courses in analysis and stochastic processes. His research lies in the area of stochastic analysis. A recent book authored by him is Markov Processes, Feller Semigroups and Evolution Equations, published by WSPC, Singapore, 2011, of about 800 pages.
The embed frame is free to use for private persons, universities and schools. It is not allowed to be used by any company for commercial purposes unless it is for media coverage. You may not modify, build upon, or block any portion or functionality of the embed frame, including but not limited to links back to the bookboon.com website.
The Embed frame may not be used as part of a commercial business offering. The embed frame is intended for private people who want to share eBooks on their website or blog, professors or teaching professionals who want to make an eBook available directly on their page, and media, journalists or bloggers who wants to discuss a given eBook
If you are in doubt about whether you can implement the embed frame, you are welcome to contact Thomas Buus Madsen on firstname.lastname@example.org and seek permission.
victor okai ★★★★★
It is very good and useful to scientists and engineers.