Fatou Theory in Two Dimensions
Author: Krastio Lilov
Publisher:
Published: 2004
Total Pages: 242
ISBN-13:
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Author: Krastio Lilov
Publisher:
Published: 2004
Total Pages: 242
ISBN-13:
DOWNLOAD EBOOKAuthor: Manfred Einsiedler
Publisher: Springer Nature
Published:
Total Pages: 232
ISBN-13: 3031620143
DOWNLOAD EBOOKAuthor: Peter Des Barres March
Publisher: Ann Arbor, Mich. : University Microfilms International
Published: 1983
Total Pages: 140
ISBN-13:
DOWNLOAD EBOOKAuthor: Paul M. Gauthier
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 565
ISBN-13: 9401109346
DOWNLOAD EBOOKProceedings of the NATO Advanced Study Institute and Séminaire de mathématiques supérieures, Montréal, Canada, July 26--August 6, 1993
Author: Yi-Zhi Huang
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 289
ISBN-13: 1461242762
DOWNLOAD EBOOKThe theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical struc- tures of conformal field theories. Much of the recent progress has deep connec- tions with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Vir as oro and affine Kac- Moody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on.He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a big and important problem. On the one hand, the theory of vertex operator algebras and their repre- sentations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions.
Author: Rolf Berndt
Publisher: Springer Science & Business Media
Published: 1998
Total Pages: 236
ISBN-13: 9783764359225
DOWNLOAD EBOOKThe Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve. This text gathers for the first time material from the representation theory of this group in both local (archimedean and non-archimedean) cases and in the global number field case. Via a bridge to Waldspurger's theory for the metaplectic group, complete classification theorems for irreducible representations are obtained. Further topics include differential operators, Whittaker models, Hecke operators, spherical representations and theta functions. The global theory is aimed at the correspondence between automorphic representations and Jacobi forms. This volume is thus a complement to the seminal book on Jacobi forms by M. Eichler and D. Zagier. Incorporating results of the authors' original research, this exposition is meant for researchers and graduate students interested in algebraic groups and number theory, in particular, modular and automorphic forms.
Author: Alberto Facchini
Publisher: Springer Science & Business Media
Published: 1998-06-16
Total Pages: 312
ISBN-13: 9783764359089
DOWNLOAD EBOOKThis expository monograph was written for three reasons. Firstly, we wanted to present the solution to a problem posed by Wolfgang Krull in 1932 [Krull 32]. He asked whether what we now call the "Krull-Schmidt Theorem" holds for ar tinian modules. The problem remained open for 63 years: its solution, a negative answer to Krull's question, was published only in 1995 (see [Facchini, Herbera, Levy and Vamos]). Secondly, we wanted to present the answer to a question posed by Warfield in 1975 [Warfield 75]. He proved that every finitely pre sented module over a serial ring is a direct sum of uniserial modules, and asked if such a decomposition was unique. In other words, Warfield asked whether the "Krull-Schmidt Theorem" holds for serial modules. The solution to this problem, a negative answer again, appeared in [Facchini 96]. Thirdly, the so lution to Warfield's problem shows interesting behavior, a rare phenomenon in the history of Krull-Schmidt type theorems. Essentially, the Krull-Schmidt Theorem holds for some classes of modules and not for others. When it does hold, any two indecomposable decompositions are uniquely determined up to a permutation, and when it does not hold for a class of modules, this is proved via an example. For serial modules the Krull-Schmidt Theorem does not hold, but any two indecomposable decompositions are uniquely determined up to two permutations. We wanted to present such a phenomenon to a wider math ematical audience.
Author: Tadeusz Iwaniec
Publisher: Clarendon Press
Published: 2001
Total Pages: 576
ISBN-13: 9780198509295
DOWNLOAD EBOOKIwaniec (math, Syracuse U.) and Martin (math, U. of Auckland) explain recent developments in the geometry of mappings, related to functions or deformations between subsets of the Euclidean n-space Rn and more generally between manifolds or other geometric objects. Material on mappings intersects with aspects of differential geometry, topology, partial differential equations, harmonic analysis, and the calculus of variations. Chapters cover topics such as conformal mappings, stability of the Mobius group, Sobolev theory and function spaces, the Liouville theorem, even dimensions, Picard and Montel theorems in space, uniformly quasiregular mappings, and quasiconformal groups. c. Book News Inc.
Author: John Erik Fornaess
Publisher: Springer Science & Business Media
Published: 2004
Total Pages: 236
ISBN-13: 9783540223580
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