Pseudo-differential operators and existence of Gabor frames
نویسندگان
چکیده
منابع مشابه
Integral Operators, Pseudodifferential Operators, and Gabor Frames
This chapter illustrates the use of Gabor frame analysis to derive results on the spectral properties of integral and pseudodifferential operators. In particular, we obtain a sufficient condition on the kernel of an integral operator or the symbol of a pseudodifferential operator which implies that the operator is trace-class. This result significantly improves a sufficient condition due to Dau...
متن کاملThe Existence of Gabor Bases and Frames
For an arbitrary full rank lattice Λ in R and a function g ∈ L(R) the Gabor (or Weyl-Heisenberg) system is G(Λ, g) := {eg(x − κ) ̨ ̨ (κ, `) ∈ Λ}. It is well-known that a necessary condition for G(Λ, g) to be an orthonormal basis for L(R) is that the density of Λ has D(Λ) = 1. However, except for symplectic lattices it remains an unsolved question whether D(Λ) = 1 is sufficient for the existence o...
متن کاملNonstationary Gabor frames - Existence and construction
Nonstationary Gabor frames were recently introduced in [2] and represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. In this paper we show a general existence result for this family of frames. We also construct nonstationary Gabor frames with non-compactly supported windows from a related painless nonorthogona...
متن کاملproperties of M−hyoellipticity for pseudo differential operators
In this paper we study properties of symbols such that these belong to class of symbols sitting insideSm ρ,φ that we shall introduce as the following. So for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of M−hypoelliptic pseudodifferential operators for which define base on this class of symbols. Also we consider maxi...
متن کاملAutomorphic Pseudo-differential Operators
For recent developments of this work in the classical direction, especially to generalizing to modular groups acting on higher dimensional spaces, see papers of Min Ho Lee: http://www.math.uni.edu/ lee/pub.html. He has, for example, developed the Hilbert modular case. Also, Olav Richter’s work on Rankin-Cohen brackets: http://www.math.unt.edu/ richter/. Work of Conley on 1/2-integral weight: ht...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pseudo-Differential Operators and Applications
سال: 2019
ISSN: 1662-9981,1662-999X
DOI: 10.1007/s11868-019-00279-1