An Endpoint $(1,\infty)$ Balian-Low Theorem
نویسندگان
چکیده
منابع مشابه
Differentiation and the Balian{low Theorem
\If it is true, it can be proved." | Enrico Fermi ABSTRACT. The Balian{Low theorem (BLT) is a key result in time-frequency analysis, originally stated by Balian and, independently, by Low, as: If a Gabor system fe 2imbt g(t ? na)g m;n2Z with ab = 1 forms an orthonormal basis for L 2 (R), then Z 1 ?1 jtg(t)j 2 dt Z 1 ?1 j ^ g()j 2 dd = +1: The BLT was later extended from orthonormal bases to exa...
متن کاملA Critical-exponent Balian-low Theorem
Using a variant of the Sobolev Embedding Theorem, we prove an uncertainty principle related to Gabor systems that generalizes the Balian-Low Theorem. Namely, if f ∈ H(R) and f̂ ∈ H /2(R) with 1 < p < ∞, 1 p + 1 p′ = 1, then the Gabor system G(f, 1, 1) is not a frame for L(R). In the p = 1 case, we obtain a generalization of the result in [BCPS].
متن کاملStudy of an Optimal Example for the Balian–Low Theorem
We analyze the time-frequency concentration of the Gabor orthonormal basis G(f,1,1) constructed by Høholdt, Jensen, and Justesen. We prove that their window function f has near optimal time and frequency localization with respect to a non-symmetric version of the Balian-Low Theorem. In particular, we show that if (p, q) = (3/2,3), then R |t||f(t)|dt < ∞, and R |γ|| b f(γ)|dγ < ∞, for 0 < ǫ ≤ 3/...
متن کاملGabor Schauder Bases and the Balian–low Theorem
The Balian–Low Theorem is a strong form of the uncertainty principle for Gabor systems which form orthonormal or Riesz bases for L(R). In this paper we investigate the Balian–Low Theorem in the setting of Schauder bases. We prove that new weak versions of the Balian–Low Theorem hold for Gabor Schauder bases, but we constructively demonstrate that several variants of the BLT can fail for Gabor S...
متن کاملDilation of the Weyl Symbol and Balian-low Theorem
The key result of this paper describes the fact that for an important class of pseudodifferential operators the property of invertibility is preserved under minor dilations of their Weyl symbols. This observation has two implications in time-frequency analysis. First, it implies the stability of general Gabor frames under small dilations of the time-frequency set, previously known only for the ...
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: Mathematical Research Letters
سال: 2006
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2006.v13.n3.a11