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Theta functions play a major role in many current researches and are powerful tools for studying integrable systems. The purpose of this paper is to provide a short and quick exposition of some aspects of meromorphic theta functions for…
Based on a new generalization of Cauchy-Riemann system presented in this paper, we introduce a class of quaternion-valued functions of a quaternionic variable, which are called algebraic regular functions. The set of algebraic regular…
Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value…
In this paper, we establish some Strichartz estimates for orthonormal functions and probabilistic convergence of density functions related to compact operators on manifolds. Firstly, we present the suitable bound of $\int_{a\leq|s|\leq…
On $\mathbb{R}^n,$ a classical result due to Bourgain establishes the restricted weak $(\frac{n}{n-1},1)$ inequality for the full maximal function $M_F^{d\sigma}$ associated to the spherical averages. In this work we present an extension to…
A review is made of the basic tools used in mathematics to define a calculus for pseudodifferential operators on Riemannian manifolds endowed with a connection: esistence theorem for the function that generalizes the phase; analogue of…
In this paper, we consider optimizing a smooth, convex, lower semicontinuous function in Riemannian space with constraints. To solve the problem, we first convert it to a dual problem and then propose a general primal-dual algorithm to…
The higher step Grushin operators $\Delta_{\alpha}$ are a family of sub-elliptic operators which degenerate on a sub-manifold of $\mathbb{R}^{n+m}$. This paper establishes Carleman-type inequalities for these operators. It is achieved by…
A consistent approach to the description of integral coordinate invariant functionals of the metric on manifolds ${\cal M}_{\alpha}$ with conical defects (or singularities) of the topology $C_{\alpha}\times\Sigma$ is developed. According to…
This thesis explores an exotic class of M-theory compactifications in which the compact manifold is taken to be a Calabi-Yau five-fold. The resulting effective theory is a one-dimensional N=2 super-mechanics model that exhibits peculiar…
In this work, we consider certain class of bi-univalent functions related with shell-like curves related to $\kappa-$Fibonacci numbers. Further, we obtain the estimates of initial Taylor-Maclaurin coefficients (second and third…
We introduce the new notion of a conjugate weight function and provide a detailed study of this operation and its properties. Then we apply this knowledge to study classes of ultradifferentiable functions defined in terms of fast growing…
A conceptual framework involving partition functions of normal factor graphs is introduced, paralleling a similar recent development by Al-Bashabsheh and Mao. The partition functions of dual normal factor graphs are shown to be a Fourier…
Computing explicitly the {\epsilon}-subdifferential of a proper function amounts to computing the level set of a convex function namely the conjugate minus a linear function. The resulting theoretical algorithm is applied to the the class…
We characterize the common range of the adjoints of cyclic multiplication operators on the Drury--Arveson space. We show that a function belongs to this common range if and only if its Taylor coefficients satisfy a simple decay condition.…
In this paper we study the class $\mathcal{E}_{m}(\Omega)$ of $m-$subharmonic functions introduced by Lu in \cite{L1}. We prove that the convergence in $m-$capacity implies the convergence of the associated Hessian measure for functions…
We extend the definition of analytic and Reidemeister torsion from closed compact Riemannian manifolds to compact Riemannian manifolds with boundary $(M, \partial M)$, given a flat bundle $\Cal F$ of $\Cal A$-Hilbert modules of finite type…
We consider Toeplitz operators associated with the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle on a compact symplectic manifold. We study the asymptotic behavior, in the semiclassical limit, of low-lying…
The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of…
A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied,…