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We show how Langevin diffusions can be interpreted in the context of stochastic Hamiltonian systems with structure-preserving noise and dissipation on reductive Lie groups. Reductive Lie groups provide the setting in which the Lie group…

Probability · Mathematics 2025-09-15 Erwin Luesink , Oliver D. Street

Motivated by Dunkl operators theory, we consider a generating series involving a modified Bessel function and a Gegenbauer polynomial, that generalizes a known series already considered by L. Gegenbauer. We actually use inversion formulas…

Classical Analysis and ODEs · Mathematics 2012-07-30 Nizar Demni

The goal of this paper is to describe the $\alpha$-cosine transform on functions on a Grassmannian of $i$-planes in an $n$-dimensional real vector space. in analytic terms as explicitly as possible. We show that for all but finitely many…

Metric Geometry · Mathematics 2016-05-06 Semyon Alesker , Dmitry Gourevitch , Siddhartha Sahi

We establish a mixed norm estimate for the Radon transform in the plane when the set of directions has fractional dimension. This estimate is used to prove a result about an exceptional set of directions connected with projections of planar…

Classical Analysis and ODEs · Mathematics 2019-08-15 Daniel M. Oberlin

The renormalization group is the cornerstone of the modern theory of universality and phase transitions, a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its network counterpart is…

Statistical Mechanics · Physics 2023-01-11 Pablo Villegas , Tommaso Gili , Guido Caldarelli , Andrea Gabrielli

Simulating the radar illumination of large scenes generally relies on a geometric model of light transport which largely ignores prominent wave effects. This can be remedied through coherence ray-tracing, but this requires the Wigner…

Robotics · Computer Science 2022-02-08 Jacob Mackay , David Johnson , Graham Brooker

Making use of theory of differentiable stacks, we study symplectic vortex equations over a compact orbifold Riemann surface. We discuss the category of representable morphisms from a compact orbifold Riemann surface to a quotient stack.…

Symplectic Geometry · Mathematics 2012-06-29 Hironori Sakai

In this work we study representations of the Poincare group defined over symplectic manifolds, deriving the Klein-Gordon and the Dirac equation in phase space. The formalism is associated with relativistic Wigner functions; the Noether…

High Energy Physics - Theory · Physics 2008-11-26 R. G. G. Amorim , M. C. B. Fernandes , F. C. Khanna , A. E. Santana , J. D. M. Vianna

Novel analysis of finite dimensional Hilbert space is outlined. The approach bypasses general, inherent, difficulties present in handling angular variables in finite dimensional problems: The finite dimensional, d, Hilbert space operators…

Quantum Physics · Physics 2016-11-26 M. Revzen

We study the cohomology of the complexes of differential, integral and pseudo forms on odd symplectic manifolds taking the wedge product with the symplectic form as differential. We show that the cohomology classes are in correspondence…

High Energy Physics - Theory · Physics 2021-04-21 R. Catenacci , C. A. Cremonini , P. A. Grassi , S. Noja

We study the Segal-Bargmann transform on a motion group Rn n K; where K is a compact subgroup of SO(n): A characterization of the Poisson integrals associated to the Laplacian on Rn n K is given. We also establish a Paley-Wiener type…

Functional Analysis · Mathematics 2010-01-14 Suparna Sen

Selfdual representations of any group fall into two classes when they are irreducible: those which carry a symmetric bilinear form, and the others which carry an alternating bilinear form. The Langlands correspondence, which matches the…

Number Theory · Mathematics 2008-07-03 Dipendra Prasad , Dinakar Ramakrishnan

The article suggests a new approach what is called a consistency method for the inversion of the spherical Radon transform in 2D with detectors on a line. It is known that there is not an exact inversion formula in 2D. By means of the…

Numerical Analysis · Mathematics 2017-05-31 Rafik Aramyan

We consider a completely integrable lattice regularization of the sine-Gordon model with discrete space and continuous time. We derive a determinant representation for a correlation function which in the continuum limit turns into the…

High Energy Physics - Theory · Physics 2008-11-26 Fabian H. L. Essler , Holger Frahm , Alexander R. Its , Vladimir E. Korepin

A novel imaging principle based on the interaction of electromagnetic waves with a beam of relativistic electrons is proposed. Wave-particle interaction is assumed to take place in a small spatial domain, so that each electron is only…

Classical Physics · Physics 2009-11-10 Neil Budko

The systematization of the purely Lagrangean approach to constrained systems in the form of an algorithm involves the iterative construction of a generalized Hessian matrix W taking a rectangular form. This Hessian will exhibit as many left…

High Energy Physics - Theory · Physics 2008-11-26 Heinz J. Rothe , Klaus D. Rothe

We characterize the range of the cosine transform on real Grassmannians in terms of the decomposition under the action of the special orthogonal group SO(n). Also a geometric interpretation of its image is given. The non- Archimedean…

Metric Geometry · Mathematics 2007-05-23 Semyon Alesker , Joseph Bernstein

Let $M$ be the space of real $n\times m$ matrices which can be identified with the Euclidean space $R^{nm}$. We introduce continuous wavelet transforms on $M$ with a multivalued scaling parameter represented by a positive definite symmetric…

Functional Analysis · Mathematics 2007-05-23 G. Olafsson , E. Ournycheva , B. Rubin

The main purpose of this article is to supplement the authors' results on degenerate principal series representations of real symplectic groups with the analogous results for metaplectic groups. The basic theme, as in the previous case, is…

Representation Theory · Mathematics 2014-06-06 Soo Teck Lee , Chen-Bo Zhu

In this paper we prove the connectedness of symplectic ball packings in the complement of a spherical Lagrangian, S^2 or RP^2, in symplectic manifolds that are rational or ruled. Via a symplectic cutting construction this is a natural…

Symplectic Geometry · Mathematics 2014-02-20 Matthew Strom Borman , Tian-Jun Li , Weiwei Wu