Author : Shek-Tung Wong
Publisher : American Mathematical Soc.
Page : 225 pages
File Size : 42,54 MB
Release : 1990
Category : Mathematics
ISBN : 0821824864
We carry out, in the context of an algebraic group and an arithmetic subgroup, an idea of Selberg for continuing Eisenstein series. It makes use of the theory of integral operators. The meromorphic continuation and functional equation of an Eisenstein series constructed with a cusp form on the Levi component of a rank one cuspidal subgroup are established.
Author : John David Fay
Publisher : American Mathematical Soc.
Page : 137 pages
File Size : 50,40 MB
Release : 1992
Category : Mathematics
ISBN : 082182550X
This memoir is a study of Ray-Singer analytic torsion for hermitian vector bundles on a compact Riemann surface [italic]C. The torsion is expressed through the trace of a modified resolvent. Thus, one can develop perturbation-curvature formulae for the Green-Szegö kernel and also for the torsion in terms of the Ahlfors-Bers complex structure of the Teichmuller space and Mumford complex structure of the moduli space of stable bundles of degree zero on [italic]C.
Author : Bruce Arie Reznick
Publisher : American Mathematical Soc.
Page : 169 pages
File Size : 43,34 MB
Release : 1992
Category : Mathematics
ISBN : 0821825232
This work initiates a systematic analysis of the representation of real forms of even degree as sums of powers of linear forms and the resulting implications in real algebraic geometry, number theory, combinatorics, functional analysis, and numerical analysis. The proofs utilize elementary techniques from linear algebra, convexity, number theory, and real algebraic geometry and many explicit examples and relevant historical remarks are presented.
Author : Steven Zelditch
Publisher : American Mathematical Soc.
Page : 113 pages
File Size : 36,70 MB
Release : 1992
Category : Curves on surfaces
ISBN : 0821825267
This work is concerned with a pair of dual asymptotics problems on a finite-area hyperbolic surface. The first problem is to determine the distribution of closed geodesics in the unit tangent bundle. The second problem is to determine the distribution of eigenfunctions (in microlocal sense) in the unit tangent bundle.
Author : Shari A. Prevost
Publisher : American Mathematical Soc.
Page : 113 pages
File Size : 10,59 MB
Release : 1992
Category : Mathematics
ISBN : 0821825275
We present a new proof of the identities needed to exhibit an explicit [bold]Z-basis for the universal enveloping algebra associated to an affine Lie algebra. We then use the explicit [bold]Z-bases to extend Borcherds' description, via vertex operator representations, of a [bold]Z-form of the enveloping algebras for the simply-laced affine Lie algebras to the enveloping algebras associated to the unequal root length affine Lie algebras.
Author : Dennis A. Hejhal
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 30,89 MB
Release : 1992
Category : Automorphic functions
ISBN : 0821825291
Paper I is concerned with computational aspects of the Selberg trace formalism, considering the usual type of eigenfunction and including an analysis of pseudo cusp forms and their residual effects. Paper II examines the modular group PSL (2, [bold]Z), as such groups have both a discrete and continuous spectrum. This paper only examines the discrete side of the spectrum.
Author : Kazuaki Taira
Publisher : American Mathematical Soc.
Page : 81 pages
File Size : 20,17 MB
Release : 1992
Category : Mathematics
ISBN : 0821825356
This paper is devoted to the functional analytic approach to the problem of construction of Feller semigroups with Ventcel' (Wentzell) boundary conditions. This paper considers the non-transversal case and solves from the viewpoint of functional analysis the problem of construction of Feller semigroups for elliptic Waldenfels operators. Intuitively, our result may be stated as follows: One can construct a Feller semigroup corresponding to such a diffusion phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it "dies" at which time it reaches the set where the absorption phenomenon occurs.
Author : Patrick Fitzpatrick
Publisher : American Mathematical Soc.
Page : 145 pages
File Size : 25,27 MB
Release : 1993-01-01
Category : Mathematics
ISBN : 0821825445
The aim of this work is to develop an additive, integer-valued degree theory for the class of quasilinear Fredholm mappings. This class is sufficiently large that, within its framework, one can study general fully nonlinear elliptic boundary value problems. A degree for the whole class of quasilinear Fredholm mappings must necessarily accommodate sign-switching of the degree along admissible homotopies. The authors introduce ''parity'', a homotopy invariant of paths of linear Fredholm operators having invertible endpoints. The parity provides a complete description of the possible changes in sign of the degree and thereby permits use of the degree to prove multiplicity and bifurcation theorems for quasilinear Fredholm mappings. Applications are given to the study of fully nonlinear elliptic boundary value problems.
Author : Thomas Callister Hales
Publisher : American Mathematical Soc.
Page : 161 pages
File Size : 49,14 MB
Release : 1992
Category : Mathematics
ISBN : 0821825399
An integral formula for the subregular germ of a [italic small capital]K-orbital integral is developed. The formula holds for any reductive group over a [italic]p-adic field of characteristic zero. This expression of the subregular germ is obtained by applying Igusa's theory of asymptotic expansions. The integral formula is applied to the question of the transfer of a [italic small capital]K-orbital integral to an endoscopic group. It is shown that the quadratic characters arising in the subregular germs are compatible with the transfer. Details of the transfer are given for the subregular germ of unitary groups.
Author : Henry C. Wente
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 20,1 MB
Release : 1992
Category : Mathematics
ISBN : 0821825364
This memoir is devoted to the case of constant mean curvature surfaces immersed in [bold]R3. We reduce this geometrical problem to finding certain integrable solutions to the Gauss equation. Many new and interesting examples are presented, including immersed cylinders in [bold]R3 with embedded Delaunay ends and [italic]n-lobes in the middle, and one-parameter families of immersed constant mean curvature tori in [bold]R3. We examine minimal surfaces in hyperbolic three-space, which is in some ways the most complicated case.
