TY - BOOK ID - 77929140 TI - Multivariate Characteristic and Correlation Functions PY - 2013 VL - 50 SN - 01790986 SN - 3110223996 9783110223996 9783110223989 3110223988 PB - Berlin Boston DB - UniCat KW - Characteristic functions. KW - Correlation (Statistics) KW - Variables (Mathematics) KW - Multivariate analysis. KW - Multivariate distributions KW - Multivariate statistical analysis KW - Statistical analysis, Multivariate KW - Analysis of variance KW - Mathematical statistics KW - Matrices KW - Mathematical constants KW - Mathematics KW - Least squares KW - Probabilities KW - Regression analysis KW - Statistics KW - Instrumental variables (Statistics) KW - Characteristic formula of an ideal KW - Characteristic Hilbert functions KW - Functions, Characteristic KW - Functions, Hilbert KW - Hilbert characteristic functions KW - Hilbert functions KW - Hilbert's characteristic functions KW - Hilbert's functions KW - Postulation formula KW - Graphic methods KW - Characteristic Functions. KW - Fourier Transform. KW - Moment Problem. KW - Probability Distribution. UR - https://www.unicat.be/uniCat?func=search&query=sysid:77929140 AB - In a certain sense characteristic functions and correlation functions are the same, the common underlying concept is positive definiteness. Many results in probability theory, mathematical statistics and stochastic processes can be derived by using these functions. While there are books on characteristic functions of one variable, books devoting some sections to the multivariate case, and books treating the general case of locally compact groups, interestingly there is no book devoted entirely to the multidimensional case which is extremely important for applications. This book is intended to fill this gap at least partially. It makes the basic concepts and results on multivariate characteristic and correlation functions easily accessible to both students and researchers in a comprehensive manner. The first chapter presents basic results and should be read carefully since it is essential for the understanding of the subsequent chapters. The second chapter is devoted to correlation functions, their applications to stationary processes and some connections to harmonic analysis. In Chapter 3 we deal with several special properties, Chapter 4 is devoted to the extension problem while Chapter 5 contains a few applications. A relatively large appendix comprises topics like infinite products, functional equations, special functions or compact operators. ER -