Related papers: Moutard transform approach to generalized analytic…
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
Functional integrals are defined in terms of locally compact topological groups and their associated Banach-valued Haar integrals. This approach generalizes the functional integral scheme of Cartier and DeWitt-Morette. The definition allows…
We study translating soliton solutions to the flow by powers of the curvature of curves in the plane. We characterize these solitons as critical curves for functionals depending on the curvature. More precisely, translating solitons to the…
We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…
The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…
The main result of this paper is a convexity estimate for translating solitons of extrinsic geometric flows which evolve under a $1$-homogeneous concave function in the principal curvatures. In addition, we show examples of these…
Miller-Paris transformations are extensions of Euler's transformations for the Gauss hypergeometric functions to generalized hypergeometric functions of higher-order having integral parameter differences (IPD). In our recent work we…
In this paper we deal with generalizations of the Mahler volume product for log-concave functions. We show that the polarity transform $\mathcal A$ can be rescaled so that the Mahler product it induces has upper and lower bounds of the same…
We introduce a general context involving a presheaf A and a subpresheaf B of A. We show that all previously considered cases of local analysis of generalized functions (defined from duality or algebraic techniques) can be interpretated as…
In this paper, we give a description of the possible poles of the local zeta function attached to a complex or real analytic mapping in terms of a log-principalization of an ideal associated to the mapping. When the mapping is a…
Transformer-based models excel in various tasks but their generalization capabilities, especially in arithmetic reasoning, remain incompletely understood. Arithmetic tasks provide a controlled framework to explore these capabilities, yet…
We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling. This approach allows for the efficient inference of theoretical parameters in high-dimensional…
We establish universality of the renormalised energy for mappings from a planar domain to a compact manifold, by approximating subquadratic polar convex functionals of the form $\int_\Omega f(|\mathrm{D} u|)\,\mathrm{d} x$. The analysis…
An index transform, involving the square of Whittaker's function is introduced and investigated. The corresponding inversion formula is established. Particular cases cover index transforms of the Lebedev type with products of the modified…
We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms.…
These are notes of a talk based on the work arXiv:1212.3630 joint with A. Aizenbud. Let V be a finite-dimensional vector space over a local field F of characteristic 0. Let f be a function on V of the form $f(x)= \psi (P(x))$, where P is a…
We prove local inequalities for analytic functions defined on a convex body in $\Re^{n}$ which generalize well-known classical inequalities for polynomials.
Modular operads are a special type of operad: in fact, they bear the same relationship to operads that graphs do to trees (i.e. simply connected graphs). One of the basic examples of a modular operad is the collection of…
An extension of the Laplace transform obtained by using the Laguerre-type exponentials is first shown. Furthermore, the solution of the Blissard problem by means of the Bell polynomials, gives the possibility to associate to any numerical…
We give an abstract categorical treatment of Plonka sums and products using lax and oplax morphisms of monads. Plonka sums were originally defined as operations on algebras of regular theories. Their arities are sup-semilattices. It turns…