Related papers: Some quantitative versions of Ratner's mixing esti…
A complete classification is established for continuous and SL(n) covariant matrix-valued valuations on Lp(Rn,|x|2dx). The assumption of matrix symmetry is eliminated. For n>2, such valuation is uniquely characterized by the moment matrix…
Properties of analytic vectors in representations of SL(2,R) are used to give new bounds for the triple products recently considered by P. Sarnak. A conjecture of Sarnak about such products is proved. The results of this paper generalize…
The general formula for R-matrices of slq(2,C) for the highest weight repre- sentations both for general q and for q being a root of unity by generalizing G.Gomez's and G.Sierra's one for semiperiodic representations of slq(2,C) at roots of…
We consider the spectral analysis of several examples of bilateral birth-death processes and compute explicitly the spectral matrix and the corresponding orthogonal polynomials. We also use the spectral representation to study some…
In this note we mainly study the fine Jordan-Chevalley decomposition: a refinement of the classical Jordan-Chevalley decomposition of a matrix and we pay a particular attention to the field of the coefficients of the matrix. Moreover we…
We study some aspects of the representation theory of Mantaci-Reutenauer algebras: Cartan matrix, Loewy length, modular representations.
We describe derivations of several important associative and Lie rings of infinite matrices over general rings of coefficients.
We consider Fourier transforms of densities supported on curves in R^d. We obtain sharp lower and close to sharp upper bounds for the L^q decay rates.
This short note, in part of expository nature, points out several new or recent consequences of a quite nice decomposition for positive semi-definite matrices.
In this article we derive some explicit decay estimates for the dual system of a basis of functions polynomially localized in space.
We show that the coefficients of decomposition into an irreducible components of the tensor powers of level $r$ symmetric algebra of adjoint representation coincide with the Verlinder numbers. Also we construct (for $sl(2)) the…
In this paper, we prove $L^p$ decay estimates for multilinear oscillatory integrals in $\mathbb{R}^2$, establishing sharpness through a scaling argument. The result in this paper is a generalization of the previous work by Gressman and Xiao…
The numerical analysis of gradient inclusions in a compact subset of $2\times 2$ diagonal matrices is studied. Assuming that the boundary conditions are reached after a finite number of laminations and using piecewise linear finite…
The recently discovered general formulas for perturbative correlators in basic matrix models can be interpreted as the Schur-preservation property of Gaussian measures. Then substitution of Schur by, say, Macdonald polynomials, defines a…
In this paper we consider the decomposition of positive semidefinite matrices as a sum of rank one matrices. We introduce and investigate the properties of various measures of optimality of such decompositions. For some classes of positive…
In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…
I review recent developments in lattice calculations of B decay matrix elements and other related quantities.
We construct the representations of affine sl(2,R) starting from the unitary representations of the loop ax+b-group. Our approach involves a combinatorial analysis of the correlation functions of the generators and renormalization of the…
We derive the dispersion decay for solutions of the 1D discrete Schroedinger and wave equations. Based on previous works, we weaken the conditions on potentials.
In this paper we establish a connection between the associated variety of a representation and the existence of certain degenerate Whittaker functionals, for both smooth and K-finite vectors, for all quasi-split real reductive groups,…