Related papers: Weight-Shifting Operators of Hypergeometric Type f…
We construct Hecke operators acting on Maass waveforms of integer non-zero weight and transforming according to a non-trivial multiplier system on the modular group. Using these Hecke operators we obtain multiplicativity relations for the…
We define weight changing operators for automorphic forms on Grassmannians, i.e., on orthogonal groups, and investigate their basic properties. We then evaluate their action on theta kernels, and prove that theta lifts of modular forms, in…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…
We investigate the properties of Hecke operator for sesquiharmonic Maass forms. We begin by proving Hecke equivariance of the divisor lifting with respect to sesquiharmonic Mass functions, which maps an integral weight meromorphic modular…
We compute generators and relations for a certain $2$-adic Hecke algebra of level $8$ associated with the double cover of $\mathrm{SL}_2$ and a $2$-adic Hecke algebra of level $4$ associated with $\mathrm{PGL}_2$. We show that these two…
We implement modular flavor symmetries within the Standard Model Effective Field Theory (SMEFT) framework, using the flavor group $A_4^{(q)} \times A_4^{(e)}$ with distinct moduli $\tau_q$ and $\tau_e$, and assigning different modular…
Classical Hecke operators on Maass forms are unitarely equivalent, up to a commuting phase, to completely positive maps on II$_1$ factors, associated to a pair of isomorphic subfactors, and an intertwining unitary. This representation is…
Given parameters $x \notin \mathbb{R}^- \cup \{1\}$ and $\nu$, $\mathrm{Re}(\nu) < 0$, and the space $\mathscr{H}_0$ of entire functions in $\mathbb{C}$ vanishing at $0$, we consider the family of operators $\mathfrak{L} = c_0 \cdot \delta…
Metaplectic operators form a relevant class of operators appearing in different applications, in the present work we study their Schwartz kernels. Namely, diagonality of a kernel is defined by imposing rapid off-diagonal decay conditions,…
We carry out a thorough study of weight-shifting operators on Hilbert modular forms in characteristic $p$, generalizing the author's prior work with Sasaki to the case where $p$ is ramified in the totally real field $F$. In particular we…
The conformal powers of the Laplacian of a Riemannian metric which are known as the GJMS-operators admit a combinatorial description in terms of the Taylor coefficients of a natural second-order one-parameter family $\H(r;g)$ of…
In this paper we study the boundedness in weighted variable Lebesgue spaces of operators associated with the semigroup generated by the time-independent Schr\"odinger operator $\mathcal{L}=-\Delta+V$ in $\mathbb{R}^d$, where $d>2$ and the…
Symmetric Positive Definite (SPD) matrices are ubiquitous in data analysis under the form of covariance matrices or correlation matrices. Several O(n)-invariant Riemannian metrics were defined on the SPD cone, in particular the kernel…
The unitary equivalence of $2$-isometric operators satisfying the so-called kernel condition is characterized. It relies on a model for such operators built on operator valued unilateral weighted shifts and on a characterization of the…
A representation for integral kernels of Delsarte transmutation operators is obtained in the form of a functional series with the exact formulas for the terms of the series. It is based on the application of hyperbolic pseudoanalytic…
We consider the standard hypergeometric differential operator $D$ regarded as an operator on the complex plane $C$ and the complex conjugate operator $\overline D$. These operators formally commute and are formally adjoint one to another…
Let $0\leq \alpha<n$, $m\in \mathbb{N}$ and let consider $T_{\alpha,m}$ be a of integral operator, given by kernel of the form $$K(x,y)=k_1(x-A_1y)k_2(x-A_2y)\dots k_m(x-A_my),$$ where $A_i$ are invertible matrices and each $k_i$ satisfies…
Both Feynman integrals and holographic Witten diagrams can be represented as multivariable hypergeometric functions of a class studied by Gel'fand, Kapranov & Zelevinsky known as GKZ or $\mathcal{A}$-hypergeometric functions. Among other…
We provide a full characterization in terms of the six parameters involved the boundedness of all standard weighted integral operators induced by harmonic Bergman-Besov kernels acting between different Lebesgue classes with standard weights…
We reinvestigate the Calogero-Sutherland-type (CS-type) models and generalized hypergeometric functions. We construct the generalized CS operators for circular, Hermite, Laguerre, Jacobi and Bessel cases and establish the generalized…