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Provides a novel interdisciplinary perspective on the state of the art of ultrametric pseudodifferential equations and their applications.
Sommario
1. p-adic analysis: essential ideas and results; 2. Ultrametric geometry: cluster networks and buildings; 3. p-adic wavelets; 4. Ultrametricity in the theory of complex systems; 5. Some applications of wavelets and integral operators; 6. p-adic and ultrametric models in geophysics; 7. Recent development of the theory of p-adic dynamical systems; 8. Parabolic-type equations, Markov processes, and models of complex hierarchic systems; 9. Stochastic heat equation driven by Gaussian noise; 10. Sobolev-type spaces and pseudodifferential operators; 11. Non-archimedean white noise, pseudodifferential stochastic equations, and massive Euclidean fields; 12. Heat traces and spectral zeta functions for p-adic laplacians; References; Index.
Info autore
Andrei Y. Khrennikov is Professor of Mathematics at Linnaeus University, Sweden and Director of the multidisciplinary research group International Center for Mathematical Modeling (ICMM). His research interests include the foundations of quantum physics and quantum information, the foundations of probability (in particular, studies on negative probabilities), cognitive modeling, dynamical systems, p-adic and ultrametric models in psychology, physics, and geology. He is the author of 20 monographs and around 400 papers in mathematics, physics, biology, cognitive science, economics, and finance.Sergei V. Kozyrev is a Leading Scientific Researcher in the Department of Mathematical Physics at the Steklov Mathematical Institute, Moscow. His research interests include ultrametric analysis and applications in physics and biology, stochastic limit of quantum dynamics and quantum dissipative phenomena, and mathematical models in biology.W. A. Zúñiga Galindo is a Research Professor at the Center for Research and Advanced Studies of the National Polytechnic Institute, Mexico. He is a regular member of the Colombian Academy of Exact, Physical and Natural Sciences, and of the Mexican Academy of Sciences. He is also a member of the National System of Researchers of Mexico, National Researcher Level III. His work revolves around analysis, arithmetic and geometry over non-Archimedean fields (mainly p-adic fields) and their connections with mathematical physics and applications. He has published around 50 research articles and two books.
Riassunto
Presents the state of the art of ultrametric pseudodifferential equations, relevant not only in mathematics but also in fields such as engineering, geophysics, and physics. Results previously scattered across many diverse journals are usefully consolidated here alongside novel ideas and applications.
