Related papers: Multivariate Quadratic Transformations and the Int…

We study Bergman spaces A^2(D), their kernels and Toeplitz operators on unbounded, doubly periodic domains D in the complex plane. We establish the mapping properties of the Floquet transform operator defined in A^2(D) and derive a general…

For $G=\mathrm{SL}_2$ or $\mathrm{GL}_2$, we present explicit formulas for the nonabelian Fourier kernels on $G$, as conjectured by A. Braverman and D. Kazhdan. Additionally, we furnish explicit formulas for the orbital Hankel transform on…

Here Lq-Lp boundedness of integral operator with operator-valued kernels is studied and the main result is applied to convolution operators. Using these results Besov space regularity for Fourier multiplier operator is established.

Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and…

This paper introduces planewave density interpolation methods for the regularization of weakly singular, strongly singular, hypersingular and nearly singular integral kernels present in 3D Helmholtz surface layer potentials and associated…

Let $(\Sigma,p)$ be a pointed Riemann surface of genus $g\geq 1$. For any integer $k\geq 1$, we parametrize the space of meromorphic quadratic differentials on $\Sigma$ with a pole of order $(k+2)$ at $p$, having a connected critical graph…

One of the most interesting problems in the recent renaissance of the studies in kernel regression might be whether the kernel interpolation can generalize well, since it may help us understand the `benign overfitting henomenon' reported in…

Operators that intertwine representations of a degenerate version of the double affine Hecke algebra are introduced. Each of the representations is related to multi-variable orthogonal polynomials associated with Calogero-Sutherland type…

An isogeny class of elliptic curves over a finite field is determined by a quadratic Weil polynomial. Gekeler has given a product formula, in terms of congruence considerations involving that polynomial, for the size of such an isogeny…

Integral transforms $$(\mbox{\boldmath$H$}f)(x)=\int^\infty_0H^{m,n}_{\thinspace p,q} \left[xt\left|\begin{array}{c}(a_i,\alpha_i)_{1,p}\\[1mm](b_j,\beta_j)_{1,q} \end{array}\right.\right]f(t)dt$$ involving Fox's $H$-functions as kernels…

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $\rho$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be…

We introduce a Cherednik kernel and a hypergeometric function for integral root systems and prove their relation to spherical functions associated with Riemannian symmetric spaces of reductive Lie groups. Furthermore, we characterize the…

We investigate a quantization problem which asks for the construction of an algebra for relative elliptic problems of pseudodifferential type associated to smooth embeddings. Specifically, we study the problem for embeddings in the category…

In this work, a kernel-based surrogate for integrating Hamiltonian dynamics that is symplectic by construction and tailored to large prediction horizons is proposed. The method learns a scalar potential whose gradient enters a…

We prove a transformation formula relating two determinants involving elliptic shifted factorials. Similar determinants have been applied to multiple elliptic hypergeometric series.

We present a simple algorithm to select multivariate interpolation stencil with a Cartesian grid. We show its applicability by using this algorithm in the embedded boundary method for solving the elliptic interface problem.

We study complex interpolation of variable Triebel-Lizorkin spaces, especially we present the complex interpolation of $F_{p(\cdot),q}^{\alpha }$ and $F_{p(\cdot ),p(\cdot )}^{\alpha (\cdot )}$ spaces. Also, some limiting cases are given.

A natural class of weighted Bergman spaces on the symmetrized polydisc is isometrically embedded as a subspace in the corresponding weighted Bergman space on the polydisc. We find an orthonormal basis for this subspace. It enables us to…

A recent construction of polylogarithms on Riemann surfaces of arbitrary genus in arXiv:2306.08644 is based on a flat connection assembled from single-valued non-holomorphic integration kernels that depend on two points on the Riemann…

We derive a novel integral representations of Jacobi polynomials in terms of the Gauss hypergeometric function. Such representation is then used to give the explicit integral representation for the Heat kernel on the quantized Riemann…