Completeness Theorems for Poincaré Series in One Variable (Classic Reprint) - Tapa blanda

Completeness Theorems for Poincarà Series in One Variable (Classic Reprint)

Paperback. Condición: New. Print on Demand. This book examines studies of Poincare series, especially the investigations by H. Petersson on finitely generated Fuchsian groups. The author derives and presents relevant completeness theorems that demonstrate the spaces of theta-series of some specified kind coincide with or are dense in some space of automorphic forms. The research within this book is elementary and uses the simplest concepts from linear space theory, Petersson's scalar product, and basic potential-theoretical estimates. Also discussed are scalar products that define a canonical identification of a space with its dual and the reduction of the problem of representing or approximating a function by expressions of the form GF. The author proves a partial converse of these statements and considers discrete groups of conformal self-mappings of simply connected domains. An extension to discrete groups of conformal self-mappings of an arbitrary simply connected domain is included, along with its usefulness in describing functions for which a norm is finite. A more precise statement is offered under restrictive assumptions on the domain and group. Furthermore, the author includes a discussion of Poincare series for finitely generated Fuchsian groups with limit circles. These investigations concern cusp forms, which are functions with certain properties at cusps. The author proves a lemma corresponding to one of Petersson's 'fundamental identities' and derives a consequence in the form of a theorem. This book provides completeness theorems for Poincare series, extending and simplifying Petersson's results with potential applications in the theory of moduli. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781332782253_0

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