Representations of SU(2,1) in Fourier Term Modules

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This book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the “abelian” Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the “non-abelian” modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included. These results can be applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms. Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.

Long-Term Strength of Materials 2024

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The physics of fracture processes, which includes Fracture mechanics, is crucial for understanding the longevity and reliability of any structure, from fracture initiation to propagation and final catastrophic failure. This textbook introduces the thermodynamics of irreversible processes along with entropy to address the time dependency of fracture. Working from observations of structural failure, the book identifies the principal failure types such as brittle fracture, with considerations of solo crack initiation and crack propagation associated with collective distributed damage. The other type is ductile fracture, when a crack blunts immediately on the application of stress resulting in large deformation. The book then addresses the life of a structure in a specific environment and load condition, using irreversible thermodynamics and the entropy criterion to address cooperative fracture and novel statistical Fracture mechanics to address solo fracture. Applies well-established concepts from mechanics, absent in contemporary Fracture mechanics Uses novel concepts of mechanics, irreversible thermodynamics, and statistical Fracture mechanics The book is ideal for graduate students and design engineers in civil and materials engineering, as well as mechanical and chemical engineering. Students using the book need no more than basic college-level mechanics, mathematics, and statistics knowledge. 閱讀更少