Sum Formula For Sl 2 Over A Totally Real Number Field
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Sum Formula For Sl 2 Over A Totally Real Number Field
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Author : Roelof W. Bruggeman
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-01-21
Sum Formula For Sl 2 Over A Totally Real Number Field written by Roelof W. Bruggeman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-21 with Mathematics categories.
The authors prove a general form of the sum formula $\mathrm{SL}_2$ over a totally real number field. This formula relates sums of Kloosterman sums to products of Fourier coefficients of automorphic representations. The authors give two versions: the spectral sum formula (in short: sum formula) and the Kloosterman sum formula. They have the independent test function in the spectral term, in the sum of Kloosterman sums, respectively.
Random Sets And Invariants For Type Ii Continuous Tensor Product Systems Of Hilbert Spaces
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Author : Volkmar Liebscher
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-04-10
Random Sets And Invariants For Type Ii Continuous Tensor Product Systems Of Hilbert Spaces written by Volkmar Liebscher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-10 with Mathematics categories.
In a series of papers Tsirelson constructed from measure types of random sets or (generalised) random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying $E_0$-semigroups upto cocycle conjugacy. This paper starts from establishing the converse. So the author connects each continuous tensor product system of Hilbert spaces with measure types of distributions of random (closed) sets in $[0,1]$ or $\mathbb R_+$. These measure types are stationary and factorise over disjoint intervals. In a special case of this construction, the corresponding measure type is an invariant of the product system. This shows, completing in a more systematic way the Tsirelson examples, that the classification scheme for product systems into types $\mathrm{I}_n$, $\mathrm{II}_n$ and $\mathrm{III}$ is not complete. Moreover, based on a detailed study of this kind of measure types, the author constructs for each stationary factorising measure type a continuous tensor product system of Hilbert spaces such that this measure type arises as the before mentioned invariant.
Scattering Resonances For Several Small Convex Bodies And The Lax Phillips Conjecture
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Author : Luchezar N. Stoyanov
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Scattering Resonances For Several Small Convex Bodies And The Lax Phillips Conjecture written by Luchezar N. Stoyanov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This work deals with scattering by obstacles which are finite disjoint unions of strictly convex bodies with smooth boundaries in an odd dimensional Euclidean space. The class of obstacles of this type which is considered are contained in a given (large) ball and have some additional properties.
The Dynamics Of Modulated Wave Trains
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Author : A. Doelman
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
The Dynamics Of Modulated Wave Trains written by A. Doelman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The authors investigate the dynamics of weakly-modulated nonlinear wave trains. For reaction-diffusion systems and for the complex Ginzburg-Landau equation, they establish rigorously that slowly varying modulations of wave trains are well approximated by solutions to the Burgers equation over the natural time scale. In addition to the validity of the Burgers equation, they show that the viscous shock profiles in the Burgers equation for the wave number can be found as genuine modulated waves in the underlying reaction-diffusion system. In other words, they establish the existence and stability of waves that are time-periodic in appropriately moving coordinate frames which separate regions in physical space that are occupied by wave trains of different, but almost identical, wave number. The speed of these shocks is determined by the Rankine-Hugoniot condition where the flux is given by the nonlinear dispersion relation of the wave trains. The group velocities of the wave trains in a frame moving with the interface are directed toward the interface. Using pulse-interaction theory, the authors also consider similar shock profiles for wave trains with large wave number, that is, for an infinite sequence of widely separated pulses. The results presented here are applied to the FitzHugh-Nagumo equation and to hydrodynamic stability problems.
The Moment Maps In Diffeology
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Author : Patrick Iglesias-Zemmour
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
The Moment Maps In Diffeology written by Patrick Iglesias-Zemmour and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"This memoir presents a generalization of the moment maps to the category {Diffeology}. This construction applies to every smooth action of any diffeological group G preserving a closed 2-form w, defined on some diffeological space X. In particular, that reveals a universal construction, associated to the action of the whole group of automorphisms Diff (X, w). By considering directly the space of momenta of any diffeological group G, that is the space g* of left-invariant 1-forms on G, this construction avoids any reference to Lie algebra or any notion of vector fields, or does not involve any functional analysis. These constructions of the various moment maps are illustrated by many examples, some of them originals and others suggested by the mathematical literature."--Publisher's description.
Locally Toric Manifolds And Singular Bohr Sommerfeld Leaves
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Author : Mark D. Hamilton
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Locally Toric Manifolds And Singular Bohr Sommerfeld Leaves written by Mark D. Hamilton and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"Volume 207, number 971 (first of 5 numbers)."
Approximate Homotopy Of Homomorphisms From C X Into A Simple C Algebra
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Author : Huaxin Lin
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Approximate Homotopy Of Homomorphisms From C X Into A Simple C Algebra written by Huaxin Lin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"Volume 205, number 963 (second of 5 numbers)."
Small Divisor Problem In The Theory Of Three Dimensional Water Gravity Waves
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Author : Grard Iooss
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-06-05
Small Divisor Problem In The Theory Of Three Dimensional Water Gravity Waves written by Grard Iooss and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-05 with Science categories.
The authors consider doubly-periodic travelling waves at the surface of an infinitely deep perfect fluid, only subjected to gravity $g$ and resulting from the nonlinear interaction of two simply periodic travelling waves making an angle $2\theta$ between them. Denoting by $\mu =gL/c^{2}$ the dimensionless bifurcation parameter ( $L$ is the wave length along the direction of the travelling wave and $c$ is the velocity of the wave), bifurcation occurs for $\mu = \cos \theta$. For non-resonant cases, we first give a large family of formal three-dimensional gravity travelling waves, in the form of an expansion in powers of the amplitudes of two basic travelling waves. ``Diamond waves'' are a particular case of such waves, when they are symmetric with respect to the direction of propagation. The main object of the paper is the proof of existence of such symmetric waves having the above mentioned asymptotic expansion. Due to the occurence of small divisors, the main difficulty is the inversion of the linearized operator at a non trivial point, for applying the Nash Moser theorem. This operator is the sum of a second order differentiation along a certain direction, and an integro-differential operator of first order, both depending periodically of coordinates. It is shown that for almost all angles $\theta$, the 3-dimensional travelling waves bifurcate for a set of ``good'' values of the bifurcation parameter having asymptotically a full measure near the bifurcation curve in the parameter plane $(\theta,\mu ).$
Unitary Invariants In Multivariable Operator Theory
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Author : Gelu Popescu
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-06-05
Unitary Invariants In Multivariable Operator Theory written by Gelu Popescu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-05 with Mathematics categories.
This paper concerns unitary invariants for $n$-tuples $T:=(T_1,\ldots, T_n)$ of (not necessarily commuting) bounded linear operators on Hilbert spaces. The author introduces a notion of joint numerical radius and works out its basic properties. Multivariable versions of Berger's dilation theorem, Berger-Kato-Stampfli mapping theorem, and Schwarz's lemma from complex analysis are obtained. The author studies the joint (spatial) numerical range of $T$ in connection with several unitary invariants for $n$-tuples of operators such as: right joint spectrum, joint numerical radius, euclidean operator radius, and joint spectral radius. He also proves an analogue of Toeplitz-Hausdorff theorem on the convexity of the spatial numerical range of an operator on a Hilbert space, for the joint numerical range of operators in the noncommutative analytic Toeplitz algebra $F_n^\infty$.
Twisted Pseudodifferential Calculus And Application To The Quantum Evolution Of Molecules
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Author : Andr Martinez
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-06-05
Twisted Pseudodifferential Calculus And Application To The Quantum Evolution Of Molecules written by Andr Martinez and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-05 with Mathematics categories.
The authors construct an abstract pseudodifferential calculus with operator-valued symbol, suitable for the treatment of Coulomb-type interactions, and they apply it to the study of the quantum evolution of molecules in the Born-Oppenheimer approximation, in the case of the electronic Hamiltonian admitting a local gap in its spectrum. In particular, they show that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitely. In addition, they study the propagation of certain wave packets up to long time values of Ehrenfest order.