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On the asymptotics of Hecke operators for reductive groups
In this paper, we study the asymptotic behavior of the traces of Hecke operators for spherical discrete automorphic representations of fixed level on...
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Sharp Local Smoothing Estimates for Fourier Integral Operators
The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the... -
Spaceability of the sets of surjective and injective operators between sequence spaces
We investigate algebraic structures within sets of surjective and injective linear operators between sequence spaces, completing results of Aron et...
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Quadratic Forms and Spectral Estimates
The goal of this Chapter is to provide a systematic study of quadratic forms associated with Schrödinger operators on metric graphs. -
Time Operators
A general theory of time operators is presented as part of representation theory of CCR. -
Absence of Local Unconditional Structure in Spaces of Smooth Functions on Two-Dimensional Torus
Consider a finite collection {T 1 , . . . , T J } of differential operators with constant coefficients on 𝕋 2 and the space of smooth functions generated...
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The Asymptotics of Eigenfunctions of the Absolutely Continuous Spectrum. The Scattering Problem of Three One-Dimensional Quantum Particles
In the paper the asymptotic structure of eigenfunctions of the absolutely continuous spectrum of the scattering problem is described. The case of...
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Weak Supercyclicity—An Expository Survey
This is an exposition on supercyclicity and weak supercyclicity, especially designed to advance further developments in weakly supercyclicity, which...
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Measure-operator convolutions and applications to mixed-state Gabor multipliers
For the Weyl-Heisenberg group, convolutions between functions and operators were defined by Werner as a part of a framework called quantum harmonic...
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Linear Integro-differential Equations
In this chapter, we study general elliptic operators of order 2s, which are linear and translation invariant. We start with their probabilistic... -
Some Remarks on Spectral Averaging and the Local Density of States for Random Schrödinger Operators on \(L^2 (\mathbb {R}^d)\)
We prove some local estimates on the trace of spectral projectors for random Schrödinger operators restricted to cubes...