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Related papers: Asymptotics of a Class of Operator Determinants

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We discuss the relationship between ratio asymptotics for general orthogonal polynomials and the asymptotics of the associated Bergman shift operator. More specifically, we consider the case in which a measure is supported on an infinite…

Classical Analysis and ODEs · Mathematics 2021-08-11 Brian Simanek

We define the asymptotic behavior "almost everywhere" of additive and multiplicative arithmetic functions in the paper. Classes of additive and multiplicative arithmetic functions are singled out for which the asymptotics coincides "almost…

General Mathematics · Mathematics 2023-02-02 Victor Volfson

In this paper we provide new asymptotic estimates of the Floquet exponents of Schr\"odinger operators on the circle. By the same techniques, known asymptotic estimates of various others spectral quantities are improved.

Spectral Theory · Mathematics 2011-07-25 T. Kappeler , B. Schaad , P. Topalov

Let $\Omega \subset \mathbb{R}^d$ be bounded with $C^1$ boundary. In this paper we consider Schr\"odinger operators $-\Delta+ W$ on $\Omega$ with $W(x)\approx\mathrm{dist}(x, \partial\Omega)^{-2}$ as $\mathrm{dist}(x, \partial\Omega)\to 0$.…

Spectral Theory · Mathematics 2020-10-13 Rupert L. Frank , Simon Larson

We study the asymptotics of solutions of logistic type equations with fractional Laplacian as time goes to infinity and as the exponent in nonlinear part goes to infinity. We prove strong convergence of solutions in the energy space and…

Analysis of PDEs · Mathematics 2023-08-22 Tomasz Klimsiak

We study the asymptotic behaviour of the resolvents $({\mathcal A}^\varepsilon+I)^{-1}$ of elliptic second-order differential operators ${\mathcal A}^\varepsilon$ in ${\mathbb R}^d$ with periodic rapidly oscillating coefficients, as the…

Analysis of PDEs · Mathematics 2015-09-30 Kirill Cherednichenko , Shane Cooper

We compute the asymptotic for the eigenvalues of a particular class of compact operators deeply linked with the second variation of optimal control problems. We characterize this family in terms of a set of finite dimensional data and we…

Optimization and Control · Mathematics 2022-06-08 Stefano Baranzini

In this paper, under certain restrictions on linear factors of the denominator of a rational function of two variables, the leading term of the asymptotic expansion of the coefficients is found.

Complex Variables · Mathematics 2019-11-04 Alexander Lyapin

We derive asymptotic expansion for the spectrum of Hamiltonians with a strong attractive $\delta'$ interaction supported by a smooth surface in $\R^3$, either infinite and asymptotically planar, or compact and closed. Its second term is…

Mathematical Physics · Physics 2019-12-10 Pavel Exner , Michal jex

Small perturbations of the Jacobi matrix with weights \sqrt n and zero diagonal are considered. A formula relating the asymptotics of polynomials of the first kind to the spectral density is obtained, which is analogue of the classical…

Spectral Theory · Mathematics 2010-03-19 Sergey Simonov

This paper proves an analogue of a result of Banuelos and Sa Barreto on the asymptotic expansion for the trace of Schrodinger operators on $\R^d$ when the Laplacian $\Delta$, which is the generator of the Brownian motion, is replaced by the…

Probability · Mathematics 2012-09-21 Luis Acuna Valverde

We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a nonlocal nonlinear (cubic) term in the context of symmetry analysis using the formalism of semiclassical asymptotics. This…

Mathematical Physics · Physics 2013-11-07 Aleksandr L. Lisok , Aleksandr V. Shapovalov , Andrey Yu. Trifonov

A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…

Statistics Theory · Mathematics 2008-12-18 Peter Radchenko

We generalize the Mittag-Leffler function by attaching an exponent to its Taylor coefficients. The main result is an asymptotic formula valid in sectors of the complex plane, which extends work by Le Roy [Bull. des sciences math. 24, 1900]…

Complex Variables · Mathematics 2011-03-14 Stefan Gerhold

We derive the asymptotic behavior of determinants of truncated Wiener-Hopf operators generated by symbols having Fisher-Hartwig singularities. This task is achieved thanks to an asymptotic resolution of the Riemann-Hilbert problem…

Functional Analysis · Mathematics 2022-02-22 K. K. Kozlowski

We present an asymptotic evaluation unitary formula for large argument values existing for defined class of functions. The asymptotic evaluation is obtained using only power series expansion coefficients of a function, what is a new result…

Classical Analysis and ODEs · Mathematics 2010-06-30 Mihail Nikitin

The present paper deals with a generalization of the Baskakov operators. Some direct theorems, asymptotic formula and $A$-statistical convergence are established. Our results are based on a $\rho$ function. These results include the…

Classical Analysis and ODEs · Mathematics 2016-08-08 Prashantkumar Patel , Vishnu Narayan Mishra , Mediha Örkcü

We determine the general form of the asymptotics for Dirichlet eigenvalues of the one-dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the…

Spectral Theory · Mathematics 2009-05-21 Denis Borisov , Pedro Freitas

This paper investigates the asymptotic behaviour of solutions of periodic evolution equations. Starting with a general result concerning the quantified asymptotic behaviour of periodic evolution families we go on to consider a special class…

Functional Analysis · Mathematics 2023-03-01 Lassi Paunonen , David Seifert

It is known that there is a one-to-one correspondence between equivalence classes of primitive indefinite binary quadratic forms and primitive hyperbolic conjugacy classes of the modular group. Due to such a correspondence, Sarnak obtained…

Number Theory · Mathematics 2015-02-10 Yasufumi Hashimoto