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On Abstract Spectral Constants
We prove bounds for a class of homomorphisms arising in the study of spectral sets, by involving extremal functions and vectors. These are used to...
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Spectral Galerkin Approximation
In this chapter, we describe a spectral Petrov–Galerkin method for solving the subdiffusion model ( 1.1 )....
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Spectral Gap and Dirichlet Ground State
This chapter is entirely devoted to the studies of the lowest non-trivial eigenvalue of operators on graphs. For standard Laplacians on connected...
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Spectral Sides of Trace Formulae
The Arthur-Selberg trace formula, or more generally, the relative trace formula, is an important tool in automorphic representation theory. We...
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Spectral Estimates of the Dirichlet-Laplace Operator in Conformal Regular Domains
We consider conformal spectral estimates of the Dirichlet–Laplace operator in conformal regular domains Ω ⊂ ℝ 2 , based on the geometric theory of...
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Spectral sections
The paper is devoted to the notion of a spectral section introduced by Melrose and Piazza. In the first part of the paper we generalize results of...
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Spectral Analysis of a Dynamical System Describing the Diffusion of Neutrons
AbstractThe spectral properties of the generator of an evolution semigroup describing the dynamics of particle transport in a substance are studied....
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Spectral Neural Operators
AbstractIn recent works, the authors introduced a neural operator: a special type of neural networks that can approximate maps between...
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Spectral Analysis of N-Body Schrödinger Operators at Two-Cluster Thresholds
This book provides a systematic study of spectral and scattering theory for many-body Schrödinger operators at two-cluster thresholds. While the...
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Adaptive Spectral Normalization for Generative Models
AbstractWhen using Wasserstein GAN loss function for training generative adversarial networks (GAN), it is theoretically necessary to limit the...
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An adaptive time-step** Fourier pseudo-spectral method for the Zakharov-Rubenchik equation
An adaptive time-step** scheme is developed for the Zakharov-Rubenchik system to resolve the multiple time scales accurately and to improve the...
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A Distributed Block Chebyshev-Davidson Algorithm for Parallel Spectral Clustering
We develop a distributed Block Chebyshev-Davidson algorithm to solve large-scale leading eigenvalue problems for spectral analysis in spectral...
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Sarnak’s spectral gap question
We answer in the affirmative a question of Sarnak’s from 2007, confirming that the Patterson–Sullivan base eigenfunction is the unique...
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Spectral inequality with sensor sets of decaying density for Schrödinger operators with power growth potentials
We prove a spectral inequality (a specific type of uncertainty relation) for Schrödinger operators with confinement potentials, in particular of...
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New low-rank optimization model and algorithms for spectral compressed sensing
In this paper, we investigate the recovery of an undamped spectrally sparse signal and its spectral components from a set of regularly spaced samples...
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Analysis and Hermite Spectral Approximation of Diffusive-Viscous Wave Equations in Unbounded Domains Arising in Geophysics
The diffusive-viscous wave equation (DVWE) is widely used in seismic exploration since it can explain frequency-dependent seismic reflections in a...
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Spectral decomposition and evolution equations
The spectral decomposition of the Laplacian with suitable boundary conditions gives us precise information about the solvability of the equation...