Author | Dautray, Robert. author |
---|---|
Title | Mathematical Analysis and Numerical Methods for Science and Technology [electronic resource] : Volume 2 Functional and Variational Methods / by Robert Dautray, Jacques-Louis Lions |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2000 |
Connect to | http://dx.doi.org/10.1007/978-3-642-61566-5 |
Descript | XVI, 590 p. online resource |
III. Functional Transformations -- A. Some Transformations Useful in Applications -- ยง1. Fourier Series and Dirichletโs Problem -- ยง2. The Mellin Transform -- ยง3. The Hankel Transform -- Review of Chapter III A -- B. Discrete Fourier Transforms and Fast Fourier Transforms -- ยง1. Introduction -- ยง2. Acceleration of the Product of a Matrix by a Vector -- ยง3. The Fast Fourier Transform of Cooley and Tukey -- ยง4. The Fast Fourier Transform of Good-Winograd -- ยง5. Reduction of the Number of Multiplications -- ยง6. Fast Fourier Transform in Two Dimensions -- ยง7. Some Applications of the Fast Fourier Transform -- Review of Chapter III B -- IV. Sobolev Spaces -- ยง1. Spaces H1(?), Hm(?) -- ยง2. The Space Hs(?n) -- ยง3. Sobolevโs Embedding Theorem -- ยง4. Density and Trace Theorems for the Spaces Hm(?), (m ? ? * = ?\z0{) -- ยง5. The Spaces H-m(?) for all m ? ? -- ยง6. Compactness -- ยง7. Some Inequalities in Sobolev Spaces -- ยง8. Supplementary Remarks -- Review of Chapter IV -- Appendix: The Spaces Hs(?) with ? the โRegularโ Boundary of an Open Set ? in ?n -- V. Linear Differential Operators -- ยง1. Generalities on Linear Differential Operators -- ยง2. Linear Differential Operators with Constant Coefficients -- ยง3. Cauchy Problem for Differential Operators with Constant Coefficients -- ยง4. Local Regularity of Solutions* -- ยง5. The Maximum Principle * -- Review of Chapter V -- VI. Operators in Banach Spaces and in Hilbert Spaces -- ยง1. Review of Functional Analysis: Banach and Hilbert Spaces -- ยง2. Linear Operators in Banach Spaces -- ยง3. Linear Operators in Hilbert Spaces -- Review of Chapter VI -- VII. Linear Variational Problems. Regularity -- ยง1. Elliptic Variational Theory -- ยง2. Examples of Second Order Elliptic Problems -- ยง3. Regularity of the Solutions of Variational Problems -- Review of Chapter VII -- Appendix. โDistributionsโ -- ยง1. Definition and Basic Properties of Distributions -- ยง2. Convolution of Distributions -- ยง3. Fourier Transforms -- Table of Notations -- of Volumes 1, 3โ6