Analysis and Mathematical Physics最新文献

This paper deals with developing a general spectral theory for only metrizable fuzzy normed algebras, whose topology is determined by functionals that may lack subadditivity. There are introduced the notions of fuzzy spectral radius, fuzzy boundedness radius, and fuzzy regular elements, and classical spectral results from Banach and locally convex algebras to this setting are extended. There are described fuzzy normed algebras induced by two strict t-norms and provide explicit examples, for which it is computed the fuzzy spectral radius and it is established the domain of fuzzy convergence for the Neumann series. A characterization of the fuzzy Waelbroeck resolvent set of regular elements is also given. As an application, the fuzzy Fourier transform on these algebras is investigated, proving to be a generalization of the classical transform to contexts governed by fuzzy rather than classical constraints.

We consider complete Horn hypergeometric series in two variables and present an algorithm for the determination of their domains of convergence. To this end, we start from the fundamental results due to Horn and we investigate the properties and geometry of the rational algebraic curves delimiting the Reinhardt image of the domain of convergence. Under natural restrictions on the geometry of these curves, we provide an algorithm that iteratively enumerates special subsets of the boundary of the domain of convergence. In particular, we note that the provided algorithm can be efficiently applied to determine the domains of convergence of the analytic continuations of complete hypergeometric series in two variables.

In this paper, we consider the inverse scattering problem for one-dimensional Schr(ddot{o})dinger operator on the half-line ([0,infty )) with spectral parameter dependent on boundary condition and interior discontinuous conditions. The scattering data of the problem is defined and the modified Marchenko main equation is derived. With the help of the obtained integral equations, it is shown that the potential is uniquely recovered by the given scattering data.

By utilizing constrained variational methods and analytical techniques, we investigate the existence of normalized solutions to a class of (p, q)-Laplacian equations with (L^p)-constraint, where the nonlinearity satisfies distinct weak mass supercritical conditions. Our results generalize and complement several known results in the literature. In particular, this work extends the existing results of Chen and Tang (J. Differ. Equ. 386 (2024) 435-479) and Jin and Tang (Appl. Math. Lett. 160 (2025) 109329) to the (p, q)-Laplacian setting.

The existence of weighted nontangential limits and growth rates near a polar set E of positive superharmonic functions satisfying a nonlinear inequality (-Delta u(x)le cd(x,E)^{-beta } u(x)^p) and having singularities on E are investigated. A main result extends Lions’ result (1980) regarding the asymptotic behavior near an isolated singularity of a positive solution of the Lane–Emden equation to the case of non-isolated singularities, and complements the author and Ono’s result (2014) regarding removable singularities of solutions of semilinear elliptic equations.

The paper is devoted to quadratic Poisson structures compatible with the canonical linear Poisson structures on (necessarily) trivial 1-dimensional central extensions of semisimple Lie algebras. In particular, we develop the general theory of such structures and study related families of functions in involution. We also show that there exists a 10-parametric family of quadratic Poisson structures on (mathfrak {gl}(3)^*) compatible with the canonical linear Poisson structure and containing the 3-parametric family of quadratic bivectors introduced in 2017 by Vladimir Sokolov, who showed that the corresponding involutive family of functions contains the hamiltonian of the polynomial form of the elliptic Calogero–Moser system. We also explicitly write the normal forms of the Poisson pencils in the 10-parametric family and related integrable systems. They correspond to normal forms of ternary cubic forms (degenerations of normal elliptic curve in (mathbb {P}^2)).

We consider the class of standard weighted Bergman spaces (A^2_{alpha }(mathbb {D})) and the set (SF^N(mathbb {T})) of simple partial fractions of degree N with poles on the unit circle. We prove that under certain conditions, the simple partial fractions of order N, with n poles on the unit circle attain minimal norm if and only if the points are equidistributed on the unit circle. We show that this is not the case if the conditions we impose are not met, exhibiting a new interesting phenomenon. We find sharp asymptotics for these norms. Additionally we describe the closure of these fractions in the standard weighted Bergman spaces.

This paper establishes an extended version of Heisenberg’s uncertainty principle for the Symplectic Wigner distribution via linear canonical transform (SWL), which generalizes existing Symplectic Wigner distributions. Furthermore, the properties of SWL are enumerated, and a comprehensive analysis of its Heisenberg uncertainty relation and special cases is fully elucidated. Finally, a numerical example is presented to demonstrate the efficacy of this novel distribution in detecting single-component linear frequency modulated (LFM) signals.

We construct an analogue of Dyson Brownian motion in the Siegel half-space (mathcal {H}) that we term Siegel Brownian motion. Given (beta in (0,infty ]), a stochastic flow for (Z_tin mathcal {H}) is introduced so that the law of the eigenvalues (lambda _t) of the cross ratio matrix ({mathfrak {R}}(Z_t,varvec{i}I_n)) is determined, after a change of variables to (sigma (lambda ) in (0,infty )^n), by the Itô differential equation

where (W_t) is a standard Wiener process in (mathbb {R}^n). This interacting particle system corresponds to stochastic gradient ascent

where (S(sigma )= log textrm{vol},mathcal {O}_{lambda (sigma )}) is a Boltzmann entropy that enumerates the microstates in the group orbit (mathcal {O}_lambda = {Z in mathcal {H}left| textrm{eig}left( {mathfrak {R}}(Z,varvec{i}I_n)right) =lambda right. }). In the limit (beta =infty ), the group orbits (mathcal {O}_{lambda _t}) evolve by motion by minus a half times mean curvature.