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Microlocal analysis of singular measures
The purpose of this article is to investigate the structure of singular measures from a microlocal perspective. Motivated by the result of De...
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Approximation and Interpolation of Singular Measures by Trigonometric Polynomials
Complex valued measures of finite total variation are a powerful signal model in many applications. Restricting to the d -dimensional torus, finitely...
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Singular Value Decomposition
Singular value decomposition is a fundamental result in linear algebra that has far-reaching applications in applied mathematics, statistics, and...
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A decay estimate for the Fourier transform of certain singular measures in ℝ4 and applications
We consider, for a class of functions φ : ℝ 2 { 0 } → ℝ 2 satisfying a nonisotropic homogeneity condition, the Fourier transform û of the Borel measure on...
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Inevitable monokineticity of strongly singular alignment
We prove that certain types of measure-valued map**s are monokinetic i.e. the distribution of velocity is concentrated in a Dirac mass. These...
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Singular Value Analysis of Linear Maps Under Conic Constraints
We have recently introduced and studied the concept of singular value of a rectangular matrix relative to a pair of closed convex cones. Such cones...
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Fractal Measures and Dynamics
The definitions of local, Hausdorff, and packing dimensions of a finite Borel measure on...
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An Example of Embedded Singular Continuous Spectrum for Discrete Schrödinger Operators
We present an example of a potential such that the corresponding discrete Schrödinger operator has singular continuous spectrum embedded in the...
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Transcendental Lattices of Certain Singular K3 Surfaces
We compute the transcendental lattices of the singular K3 surfaces belonging to three pencils of K3 surfaces, namely the Apéry–Fermi pencil with...
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On Singular Integral Operators with Shifts
Given p ∈ (1, ∞), the chapter is devoted to studying the Fredholmness on the space Lp( Γ) for the singular integral operator with shift...
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On Disjointly singular centralizers
We study “disjoint” versions of the notions of trivial, locally trivial, strictly singular and super-strictly singular quasi-linear maps in the...
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Singular Value Functions
This chapter is a detailed study of properties of the generalized singular value function of a...
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Spectral Measures and Dynamics: Typical Behaviors
This book convenes and deepens generic results about spectral measures, many of them available so far in scattered literature. It starts with classic...
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Reaction Forces of a Singular Pendulum
AbstractIn this paper, various types of behavior of reaction forces and Lagrange multipliers for the motion of mechanical systems with a...
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The Relaxed Stochastic Maximum Principle in Singular Optimal Control of Jump Diffusions
This paper deals with optimal control of systems driven by stochastic differential equations (SDEs), with controlled jumps, where the control...
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Form-Boundedness and SDEs with Singular Drift
We survey and refine recent results on weak and strong well-posedness of stochastic differential equations with singular drift satisfying some...
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Asymptotic Stability for Singular Diffusions
In the present chapter, asymptotic stability conditions for diffusions with linear drift and Lipschitz diffusion coefficients are presented. Although...