Related papers: Trigonometric Selector Kernels, Duality, and Odd Z…

In this paper we introduce a class of polygonal complexes for which we can define a notion of sectional combinatorial curvature. These complexes can be viewed as generalizations of 2-dimensional Euclidean and hyperbolic buildings. We focus…

Inspired by a famous formula of Ramanujan for odd zeta values, we prove an analogous formula involving the Hurwitz zeta function. We introduce a new integral kernel related to the Hurwitz zeta function, generalizing the integral kernel…

The finite dimensional representations of associative quadratic algebras with three generators are investigated by using a technique based on the deformed parafermionic oscillator algebra. One application on the calculation of the…

We establish a correspondence between vector-valued modular forms with respect to a symmetric tensor representation and quasimodular forms. This is carried out by first obtaining an explicit isomorphism between the space of vector-valued…

For odd $k$, we give a formula for the relations between double zeta values $\zeta(r,k-r)$ with $r$ even. This formula provides a connection with the space of cusp forms on $\mathrm{SL}_2(\mathbb{Z})$. This is the odd weight analogue of a…

We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction. In this work…

We obtain explicit double-contour representations for the correlation kernels of the discrete orthogonal ($\beta=1$) and symplectic ($\beta=4$) random matrix ensembles with Meixner, Charlier, and Krawtchouk weights. A single…

We study tensor products of infinite dimensional representations (not corepresentations) of the $\mathrm{SU}(2)$ quantum group. Eigenvectors of certain self-adjoint elements are obtained, and coupling coefficients between different…

We prove an explicit formula for the tensor product with itself of an irreducible complex representation of the symmetric group defined by a rectangle of height two. We also describe part of the decomposition for the tensor product of…

In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical foundation for…

We prove a number of quadratic transformations of elliptic Selberg integrals (conjectured in an earlier paper of the author), as well as studying in depth the "interpolation kernel", an analytic continuation of the author's elliptic…

We introduce some new higher dimensional generalizations of the Dedekind sums associated with the Bernoulli functions and of those Hardy sums which are defined by the sawtooth function. We generalize a variant of Parseval's formula for the…

We establish some identities of Euler related sums. By using these identities, we discuss the closed form representations of sums of harmonic numbers and reciprocal parametric binomial coefficients through parametric harmonic numbers,…

We find new representations for Itzykson-Zuber like angular integrals for arbitrary beta, in particular for the orthogonal group O(n), the unitary group U(n) and the symplectic group Sp(2n). We rewrite the Haar measure integral, as a flat…

Using realisations of the positive discrete series representations of the Lie algebra su(1,1) in terms of Meixner-Pollaczek polynomials, the action of su(1,1) on Poisson kernels of these polynomials is considered. In the tensor product of…

Spin-tomographic symbols of qudit states and spin observables are studied. Spin observables are associated with the functions on a manifold whose points are labelled by spin projections and 2-sphere coordinates. The star-product kernel for…

By using the three-term recurrence equation satisfied by a family of orthogonal polynomials, the Christoffel-Darboux-type bilinear generating function and their asymptotic expressions, we obtain quadrature formulas for integral transforms…

Torsion polynomials connect the genus of a hyperbolic knot (a topological invariant) with the discrete faithful representation (a geometric invariant). Using a new combinatorial structure of an ideal triangulation of a 3-manifold that…

We suggest a method of reduction of mixed absolute and relative boundary conditions to pure ones. The case of rank two tensor is studied in detail. For four-dimensional disk the corresponding heat kernel is expressed in terms of scalar heat…

Akemann, Ipsen and Kieburg recently showed that the squared singular values of products of M rectangular random matrices with independent complex Gaussian entries are distributed according to a determinantal point process with a correlation…