Related papers: On the Riemann-Hilbert Problem for Difference and …
We prove some existence and nonexistence results for a class of critical $(p,q)$-Laplacian problems in a bounded domain. Our results extend and complement those in the literature for model cases.
Realizing the possibility suggested by Hardouin [6], we show that her own Picard-Vessiot Theory for iterative $q$-difference rings is covered by the (consequently, more general) framework, settled by Amano and Masuoka [2], of artinian…
In this paper, under suitable settings, we can obtain the existence and uniqueness of solutions to a class of Hessian quotient equations with Dirichlet boundary condition in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$, which can be seen…
In this paper, we establish Liouville-type theorems for parabolic differential inequalities with $(p,q)-$Laplacian operator on Riemannian manifolds. By a test function argument, we establish nonexistence results under suitable weighted…
The equipartition theorem is crucial in classical statistical physics, and recent studies have revealed its quantum counterpart for specific systems. This raises the question: does a quantum counterpart of the equipartition theorem exist…
An outline of the basic Riemannian structures underlying the separation of variables in the Hamilton-Jacobi equation of natural Hamiltonian systems.
We show that a separation between the class of all problems that can efficiently be solved on a quantum computer and those solvable using probabilistic classical algorithms in polynomial time implies the generalized contextuality of quantum…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain first and second order differential equations for the orthogonal polynomials and associated functions with a weight on the unit circle. We…
A high order linear $q$-difference equation with polynomial coefficients having $q$-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation is related to the number of orthogonality conditions that these…
We study linear recurrence relations in the character solutions of $Q$-systems obtained from the Kirillov-Reshetikhin modules. We explain how known results on difference $L$-operators lead to a uniform construction of linear recurrences in…
In this article, we study the Piltz divisor problem, which is sometimes called the generalized Dirichlet divisor problem, over number fields. We establish an identity akin to Vorono\"i's formula concerning the error term in the Dirichlet…
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
We characterize the biorthogonal polynomials that appear in the theory of coupled random matrices via a Riemann-Hilbert problem. Our Riemann-Hilbert problem is different from the ones that were proposed recently by Ercolani and McLaughlin,…
The main aim of this paper is to investigate the Hardy-Littlewood type Theorem and the Heinz type inequality on functions induced by a differential operator. We first prove a more general Hardy-Littlewood type theorem for the Dirichlet…
We aim to introduce a new extension of Mittag-Leffler function via q-analogue and obtained their significant properties including integral representation, q-differentiation, q-Laplace transform, image formula under q-derivative operators.…
We formulate the inverse spectral theory of infinite gap Hill's operators with bounded periodic potential as a Riemann--Hilbert problem on a typically infinite collection of spectral bands and gaps. We establish a uniqueness theorem for…
The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat's principle in…
An elementary method of computing the values at negative integers of the Riemann zeta function is presented. The principal ingredient is a new q-analogue of the Riemann zeta function. We show that for any argument other than 1 the classical…
In this article, we investigate and establish some properties including analytic properties, contiguous relations, differential properties, differential operators, an expansion formula, and simple integrals, integral operators, some…