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| Author | : Mathematical Sciences Research Institute (Berkeley, Calif.). |
| Publisher | : |
| Total Pages | : 81 |
| Release | : 1986 |
| Genre | : |
| ISBN | : |
| Author | : Troy D. Riggs |
| Publisher | : |
| Total Pages | : 142 |
| Release | : 1993 |
| Genre | : |
| ISBN | : |
| Author | : Gerald W. Johnson |
| Publisher | : Clarendon Press |
| Total Pages | : 790 |
| Release | : 2000-03-16 |
| Genre | : Mathematics |
| ISBN | : 0191546267 |
This book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus, and also provides more detailed proofs of the central results.
| Author | : Gerald W. Johnson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 88 |
| Release | : 1986 |
| Genre | : Mathematics |
| ISBN | : 0821824139 |
The basic purpose of the paper is to construct, for the indicated integrals, series expansions in terms of finite multiple integrals of increasing multiplicity ("generalized Dyson series''). The authors study in detail the character of these expansions in the case when the measure [lowercase Greek]Eta = [lowercase Greek]Mu + [lowercase Greek]Nu contains, in addition to a continuous part [lowercase Greek]Mu, a discrete part [lowercase Greek]Nu as well. Using generalized Feynman diagrams they give a graphical description of the expansions obtained; they also describe the Banach algebra generated by the functionals under consideration and establish connections with Feynman's operational calculus.
| Author | : Gerald W. Johnson |
| Publisher | : Oxford Mathematical Monographs |
| Total Pages | : 385 |
| Release | : 2015 |
| Genre | : Biography & Autobiography |
| ISBN | : 0198702493 |
This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book. The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections with certain analytic Feynman integrals are noted. This volume is essentially self-contained and we only assume that the reader has a reasonable, graduate level, background in analysis, measure theory and functional analysis or operator theory. Much of the necessary remaining background is supplied in the text itself.
| Author | : Michel Laurent Lapidus |
| Publisher | : |
| Total Pages | : 55 |
| Release | : 1987* |
| Genre | : |
| ISBN | : |
| Author | : Sergio Albeverio |
| Publisher | : Springer |
| Total Pages | : 184 |
| Release | : 2008-05-06 |
| Genre | : Mathematics |
| ISBN | : 3540769560 |
The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.
| Author | : Stig Lundqvist |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 544 |
| Release | : 1988 |
| Genre | : Science |
| ISBN | : |
| Author | : American Mathematical Society |
| Publisher | : |
| Total Pages | : 784 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Takeyuki Hida |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 436 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461201675 |
During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, including stochastic finance, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes and reproducing kernel Hilbert space theory, and stochastic differential equations in infinite dimensions. To honor Kallianpur's pioneering work and scholarly achievements, a number of leading experts have written research articles highlighting progress and new directions of research in these and related areas. This commemorative volume, dedicated to Kallianpur on the occasion of his seventy-fifth birthday, will pay tribute to his multi-faceted achievements and to the deep insight and inspiration he has so graciously offered his students and colleagues throughout his career. Contributors to the volume: S. Aida, N. Asai, K. B. Athreya, R. N. Bhattacharya, A. Budhiraja, P. S. Chakraborty, P. Del Moral, R. Elliott, L. Gawarecki, D. Goswami, Y. Hu, J. Jacod, G. W. Johnson, L. Johnson, T. Koski, N. V. Krylov, I. Kubo, H.-H. Kuo, T. G. Kurtz, H. J. Kushner, V. Mandrekar, B. Margolius, R. Mikulevicius, I. Mitoma, H. Nagai, Y. Ogura, K. R. Parthasarathy, V. Perez-Abreu, E. Platen, B. V. Rao, B. Rozovskii, I. Shigekawa, K. B. Sinha, P. Sundar, M. Tomisaki, M. Tsuchiya, C. Tudor, W. A. Woycynski, J. Xiong.
