Related papers: Analytic Expressions and Bounds for Special Functi…
We use analytic bootstrap techniques for a CFT with an interface or a boundary. Exploiting the analytic structure of the bulk and boundary conformal blocks we extract the CFT data. We further constrain the CFT data by applying the equation…
The Theory of Functional Connections (TFC) is a functional interpolation framework founded upon the so-called constrained expression: a functional that expresses the family of all possible functions that satisfy some user-specified, linear…
Recently, there emerges different versions of beta function and hypergeometric functions containing extra parameters. Gaining enlightenment from these ideas, we will first introduce a new extension of generalized hypergeometric function and…
In this letter we discuss the analyticity properties of the Wilson-loop correlation functions relevant to the problem of soft high-energy scattering, directly at the level of the functional integral, in a genuinely nonperturbative way. The…
We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…
This paper develops a functional-analytic framework for approximating the push-forward induced by an analytic map from finitely many samples. Instead of working directly with the map, we study the push-forward on the space of locally…
We propose a conceptual frame to interpret the prolate differential operator, which appears in Communication Theory, as an entropy operator; indeed, we write its expectation values as a sum of terms, each subject to an entropy reading by an…
In this article, we introduce iterative deterministic equivalents as a novel technique for the performance analysis of communication systems whose channels are modeled by complex combinations of independent random matrices. This technique…
We propose a second-order method for unconditional minimization of functions $f(z)$ of complex arguments. We call it the Mixed Newton Method due to the use of the mixed Wirtinger derivative $\frac{\partial^2f}{\partial\bar z\partial z}$ for…
Let $\lambda$ be a positive number, and let $(x_j:j\in\mathbb Z)\subset\mathbb R$ be a fixed Riesz-basis sequence, namely, $(x_j)$ is strictly increasing, and the set of functions $\{\mathbb R\ni t\mapsto e^{ix_jt}:j\in\mathbb Z\}$ is a…
The rational solutions of the Painlev\'e-II equation appear in several applications and are known to have many remarkable algebraic and analytic properties. They also have several different representations, useful in different ways for…
Extrinsic Information Transfer (EXIT) functions can be measured by statistical methods if the message alphabet size is moderate or if messages are true a-posteriori distributions. We propose an approximation we call mixed information that…
The $q$-Whittaker function $W_\lambda(\mathbf{x};q)$ associated to a partition $\lambda$ is a $q$-analogue of the Schur function $s_\lambda(\mathbf{x})$, and is defined as the $t=0$ specialization of the Macdonald polynomial…
Most of the well-known fading distributions, if not all of them, could be encompassed by Fox's $H$-function fading. Consequently, we investigate the exact and asymptotic behavior of physical layer security (PLS) over Fox's $H$-function…
Densifying the network and deploying more antennas at each access point are two principal ways to boost the capacity of wireless networks. However, due to the complicated distributions of random signal and interference channel gains,…
Finite-temperature quantum field theories are formulated in terms of Green's functions and self-energies on the Matsubara axis. In multi-orbital systems, these quantities are related to positive semidefinite matrix-valued functions of the…
We characterize the completeness and frame/basis property of a union of under-sampled windowed exponentials of the form $$ {\mathcal F}(g): =\{e^{2\pi i n x}: n\ge 0\}\cup \{g(x)e^{2\pi i nx}: n<0\} $$ for $L^2[-1/2,1/2]$ by the spectra of…
We present analytic results for all planar two-loop Feynman integrals contributing to five-particle scattering amplitudes with one external massive leg. We express the integrals in terms of a basis of algebraically-independent…
The research presents a procedure of the closed-form average bit error rate evaluation for wireless communication systems in the presence of multipath fading. A generalization of the classical moment generating function is applied, and a…
This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of…