相关论文: Weighted finite Fourier transform operator: Unifor…

We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…

Instead of sampling a function at a single point, average sampling takes the weighted sum of function values around the point. Such a sampling strategy is more practical and more stable. In this note, we present an explicit method with an…

In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. So far, various window functions…

This paper establishes a rigorous functional analytic framework for weighted Weyl-Sonine fractional operators on semi-infinite intervals. While the classical Phillips functional calculus relies strictly on completely monotonic Bernstein…

Implementing general functions of operators is a powerful tool in quantum computation. It can be used as the basis for a variety of quantum algorithms including matrix inversion, real and imaginary-time evolution, and matrix powers. Quantum…

A previous article showed that alternative expressions for calculating oblate spheroidal radial functions of both kinds can provide accurate values over very large parameter ranges using double precision arithmetic, even where the…

This work studies the Fourier transform of the characteristic function of planar convex bodies averaged over affine transformations. We establish lower and upper bounds on the latter quantities in terms of the geometric properties of the…

Recently, Ferrulli-Laptev-Safronov (2016arXiv161205304F) obtained eigenvalue estimates for an operator associated to bilayer graphene in terms of $L^q$ norms of the (possibly non-selfadjoint) potential. They proved that for $1<q<4/3$ all…

In this work, we develop a unified framework for quasidiagonal and F\o lner-type approximations of linear operators on Hilbert spaces. These approximations (originally formulated for bounded operators and operator algebras) involve…

We study very smooth functions on the real line, namely Schwartz functions, that satisfy a finite identity relating their translates and a single modulation. Concretely, we assume there is a nontrivial linear combination of translates of…

The set of real numbers which are badly approximable by rationals admits an exhaustion by sets Bad($\epsilon$), whose dimension converges to 1 as $\epsilon$ goes to zero. D. Hensley computed the asymptotic for the dimension up to the first…

Explicit representations of the eigenvalues of the peridynamic operator have been recently derived in [5]. These representations are given in terms of generalized hypergeometric functions. Asymptotic analysis of the hypergeometric functions…

Weight decay is widely used as a regularizer in large language models, yet its precise role in shaping Transformer loss landscapes remains theoretically underexplored. This paper provides the first rigorous functional-analytic…

Fourier neural operators (FNOs) have recently been proposed as an effective framework for learning operators that map between infinite-dimensional spaces. We prove that FNOs are universal, in the sense that they can approximate any…

Let $\{e_j\}$ be an orthonormal basis of Laplace eigenfunctions of a compact Riemannian manifold $(M,g)$. Let $H \subset M$ be a submanifold and let $\{\psi_k\}$ be an orthonormal basis of Laplace eigenfunctions of $H$ with the induced…

The eigenvalue correlations of random matrices from the Jacobi Unitary Ensemble have a known asymptotic behavior as their size tends to infinity. In the bulk of the spectrum the behavior is described in terms of the sine kernel, and at the…

A uniform asymptotic theory of the free-space paraxial propagation of coherent flattened Gaussian beams is proposed in the limit of nonsmall Fresnel numbers. The pivotal role played by the error function in the mathematical description of…

The graph Fourier transform (GFT) is in general dense and requires O(n^2) time to compute and O(n^2) memory space to store. In this paper, we pursue our previous work on the approximate fast graph Fourier transform (FGFT). The FGFT is…

Let $X$ be a complete, simply connected harmonic manifold of purely exponential volume growth. This class contains all non-flat harmonic manifolds of non-positive curvature and, in particular all known examples of harmonic manifolds except…

We study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity and error estimation.