最 低 价：￥87.80
定 价：￥117.07
作 者：SalomonBochner 著 著
出 版 社：Oversea Publishing House
出版时间：2005-8-1
I S B N：9780486446202
| Chapter 1. Approximations 1.1. Approximation of functions at points 1.2. Translation functions 1.3. Approximation in norm 1.4. Vector-valued functions 1.5. Additive set functions 1.6. Periodic additive set functions Chapter 2. Fourier Expansions 2.1. Fourier integrals 2.2. Positive transforms. Plancherel transforms 2.3. Fourier series 2.4. Poisson summation formula 2.5. Summability. Heat and Laplace equations 2.6. Theta relations with spherical harmonics 2.7. Expansions in spherical harmonics 2.8. Zeta integrals 2.9. Zeta series Chapter 3. Closure Properties of Fourier Transforms 3.1. Pseudo-characters and Poisson characters 3.2. Pseudo-transforms and positive definite functions 3.3. Poisson transforms 3.4. Infinitely subdivisible processes 3.5. Absolute moments 3.6. Locally compact Abelian groups 3.7. Random variables 3.8. General positivity Chapter 4. Laplace and Mellin Transforms 4.1. Completely monotone functions in one variable 4.2. Completely monotone functions in several variables 4.3. Subordination of infinitely subdivisible processes 4.4. Subordination of Markoff processes 4.5. A theorem of Hardy, Littlewood and Paley 4.6. Functions of the Laplace operator 4.7. Multidimensional time variable 4.8. Riemann's functional equation for zeta functions 4.9. Summation formulas and Bessel functions in one and several variables Chapter 5. Stochastic Processes and Characteristic functionals 5.1. Directed sets of probability spaces 5.2. Markoff processes 5.3. Length of random paths in homogeneous spaces 5.4. Euclidean stochastic processes and their charac-teristic functionals 5.5. Random functions 5.6. Generating functionals Chapter 6. Analysis of Stochastic Processes 6.1. Basic operations with characteristic funetionals 6.2. Convergence in probability and integration 6.3. Convergence in norm 6.4. Expansion in series and integrals 6.5. Stationarity and orthogonality 6.6. Further statements Notes and References Indexes |
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