Related papers: Gaussian test functions and Jacquet-Rallis transfe…

There are two definitions of the measurable functional on the topological vector space: as a linear and measurable real-valued function and as a pointwise limit of the sequence of the continious linear functionals. In general case they are…

We propose a general theory for constructing functorial assignments $\Sigma \longmapsto \Omega_{\Sigma} \in E(\Sigma)$ for a large class of functors $E$ from a certain category of bordered surfaces to a suitable target category of…

In this paper, we present the generalized iterated function system for constructing of common fractals of generalized contractive mappings in the setup of dislocated metric spaces. The well-posedness of attractors based problems of rational…

This paper is devoted to the introduction of a new class of consistent estimators of the fractal dimension of locally self-similar Gaussian processes. These estimators are based on convex combinations of sample quantiles of discrete…

We consider the Jack--Laurent symmetric functions for special values of parameters p_0=n+k^{-1}m, where k is not rational and m and n are natural numbers. In general, the coefficients of such functions may have poles at these values of p_0.…

For the group G = PGL(2) we prove nonstandard matching and the fundamental lemma between two relative trace formulas: on one hand, the relative trace formula of Jacquet for the quotient T\G/T, where T is a nontrivial torus; on the other,…

We describe the use of generalized unitarity for the construction of correlation functions of local gauge-invariant operators in general quantum field theories and illustrate this method with several calculations in N=4 super-Yang-Mills…

Using functional equations, we define functors that generalize standard examples from calculus of one variable. Examples of such functors are discussed and their Taylor towers are computed. We also show that these functors factor through…

We will generalize the concept of aggregation function for mathematical structures as a certain function between quantales. In fact, these functions turn to be exactly the lax morphism of quantales. This provides a global framework for the…

For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size $N$, in term of a determinant; this determinant is…

In order to quantify higher-order correlations of the galaxy cluster distribution we use a complete family of additive measures which give scale-dependent morphological information. Minkowski functionals can be expressed analytically in…

We establish the existence of smooth transfer for Guo-Jacquet relative trace formulae in $p$-adic case. This kind of smooth transfer is a key step towards a generalization of Waldspurger's result on central values of L-functions of $GL_2$.

We propose a functional measure over the torsion tensor. We discuss two completely equivalent choices for the Wheeler-DeWitt supermetric for this field, the first one being based on its algebraic decomposition, the other inspired by…

Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…

Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…

After explaining the concepts of Langlands dual and miniscule representations, we define an analog of the Gauss sum for any compact, simple Lie group with a simply laced Lie algebra. We then show a reciprocity property when a Lie group is…

In this work, the commutator of any two reasonable functions of several pairs of canonical conjugate operators is obtained as a sum of terms of partial derivatives of those functions (equations 9, 10 or 11). When applied to quantum…

The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…

We construct a generalization of the theory of symmetric functions involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal…

We establish endoscopic and stable trace formulas whose discrete spectral terms are weighted by automorphic $L$-functions, by the use of basic functions that are incorporated into the global spectral and geometric coefficients. This is a…