Related papers: Spectral algorithms in higher-order Fourier analys…

Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…

This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…

A new approach to normal operators in real Hilbert spaces is discussed, and a spectral representation is obtained, derived directly from the complex case. The results are then applied to quaternionic normal operators, regarded as a special…

This paper details the purpose, difficulties, theory, implementation, and results of developing a Fast Fourier Transform (FFT) using the prime factor algorithm on an embedded system. Many applications analyze the frequency content of…

The starting point of this paper is that a spectral method is essentially a combination of an orthonormal basis of the underlying Hilbert space with Galerkin conditions. The choice of an orthonormal basis depends on a number of desirable…

Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral…

We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a…

This paper is concerned with inverse spectral problems for higher-order ($n > 2$) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either…

Inverse spectral problems are studied for the second order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and the uniqueness theorem is proved for this class of inverse problems.

Decomposition theorems in classical Fourier analysis enable us to express a bounded function in terms of few linear phases with large Fourier coefficients plus a part that is pseudorandom with respect to linear phases. The Goldreich-Levin…

Classical spectral theory provides powerful tools for analyzing linear operators, but does not extend naturally to nonlinear or compositional settings. In particular, there is no general way to transport spectral invariants in a functorial…

We prove a structure theorem for multiplicative functions which states that an arbitrary bounded multiplicative function can be decomposed into two terms, one that is approximately periodic and another that has small Gowers uniformity norm…

Data are represented as graphs in a wide range of applications, such as Computer Vision (e.g., images) and Graphics (e.g., 3D meshes), network analysis (e.g., social networks), and bio-informatics (e.g., molecules). In this context, our…

We give a spectral algorithm for decomposing overcomplete order-4 tensors, so long as their components satisfy an algebraic non-degeneracy condition that holds for nearly all (all but an algebraic set of measure $0$) tensors over…

We develop fast spectral algorithms for tensor decomposition that match the robustness guarantees of the best known polynomial-time algorithms for this problem based on the sum-of-squares (SOS) semidefinite programming hierarchy. Our…

We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral…

We introduce a new approach to the spectral equivalence of Gaussian processes and fields, based on the methods of operator theory in Hilbert space. Besides several new results including identities in law of quadratic norms for integrated…

We study a new linear up to quadratic time algorithm for linear regression in the absence of strong assumptions on the underlying distributions of samples, and in the presence of outliers. The goal is to design a procedure which comes with…

General, especially spectral, features of compact normal operators in quaternionic Hilbert spaces are studied and some results are established which generalize well-known properties of compact normal operators in complex Hilbert spaces.…

Usually such area of mathematics as differential equations acts as a consumer of results given by functional analysis. This article will give an example of the reverse interaction of these two fields of knowledge. Namely, the derivation and…