Supports of Representations in the Cohen Class

In this paper we consider a version of the uncertainty principle concerning limitations on the supports of time-frequency representations in the Cohen class. In particular we obtain various classes of kernels with the property that the corresponding representations of non trivial signals cannot be compactly supported. As an application of our results we show that a linear partial differential operator applied to the Wigner distribution of a function f≠0 in the Schwartz class cannot produce a compactly supported function.     

Uncertainty Principles in Hilbert Spaces

In this article we provide several generalizations of inequalities bounding the commutator of two linear operators acting on a Hilbert space which relate to the Heisenberg uncertainty principle and time/frequency analysis of periodic functions. We develop conditions that ensure these inequalities are sharp and apply our results to concrete examples of importance in the literature.     

Uncertainty Principles for the Ambiguity Function

We extend uncertainty principles which are valid for the Fouriertransform to the setting of the ambiguity function. A generalresult is established for annihilating sets: strongly/weaklyannihilating sets for the Fourier transform yield such setsfor the ambiguity function, extending a result known for setsof finite measure. We apply this to sublevel sets of nondegeneratequadratic forms. Our main result is a sharp version of Beurling'suncertainty principle for the ambiguity function.     

Uncertainty Principles for the Segal-Bargmann Transform

We recall some properties of the Segal-Bargmann transform; and we establish for this transform qualitative uncertainty principles: local uncertainty principle, Heisenberg uncertainty principle, Donoho-Stark''s uncertainty principle and Matolcsi-Sz\"ucs uncertainty principle.     

Prym Representations of Mapping Class Groups

Let S be a closed orientable surface of genus at least 2 and let to S be a connected finite abelian covering with covering group $G$. The lifts of liftable mapping classes of S determine a central extension (by G) of a subgroup of finite index of the mapping class group of S. This extension acts on H₁( ). With a few exceptions for genus 2, we determine the Zariski closure of the image of this representation, and prove that the image is an arithmetic group.     

Weak Uncertainty Principles on Fractals

We use the analytic tools such as the energy, and the Laplacians defined by Kigami for a class of post-critically finite (pcf) fractals which includes the Sierpinski gasket (SG), to establish some uncertainty relations for functions defined on these fractals. Although the existence of localized eigenfunctions on some of these fractals precludes an uncertainty principle in the vein of Heisenberg’s inequality, we prove in this article that a function that is localized in space must have high energy, and hence have high frequency components. We also extend our result to functions defined on products of pcf fractals, thereby obtaining an uncertainty principle on a particular type of non-pcf fractal.     

Weighted Uncertainty Principles in L

We determine sufficient conditions on positive weights W and V such that there exists continuous, strictly increasing functions Φ and Ψ on [0, ∞) such that Φ(0)=0=Ψ(0) and whenever f: R→R is a continuous integrable function. We also give an example that shows the optimality of our conditions.     

Discrete Uncertainty Principles and Sparse Signal Processing

We develop new discrete uncertainty principles in terms of numerical sparsity, which is a continuous proxy for the 0-norm. Unlike traditional sparsity, the continuity of numerical sparsity naturally accommodates functions which are nearly sparse. After studying these principles and the functions that achieve exact or near equality in them, we identify certain consequences in a number of sparse signal processing applications.     

Quasi-Permutation Representations of p-Groups of Class 2

If G is a finite linear group of degree n, that is, a finitegroup of automorphisms of an n-dimensional complex vector space(or, equivalently, a finite group of non-singular matrices oforder n with complex coefficients), we shall say that G is aquasi-permutation group if the trace of every element of G isa non-negative rational integer. The reason for this terminologyis that, if G is a permutation group of degree n, its elements,considered as acting on the elements of a basis of an n-dimensionalcomplex vector space V, induce automorphisms of V forming agroup isomorphic to G. The trace of the automorphism correspondingto an element x of G is equal to the number of letters leftfixed by x, and so is a non-negative integer. Thus, a permutationgroup of degree n has a representation as a quasi-permutationgroup of degree n. See [8].     

幂零Lie群上的不定性原理

设N是具有平方可积表示的幂零Lie群,是其Plancherel测度．本文将N上群Fourier变换矩阵化,并由此给出N上不定性原理的一种定量描述．此外,还对N上不定性原理的定性描述（简称QUP）作了讨论,结果显示出N上QUP与P（λ）的零点集之代数、几何性质的一些联系.     

The Action of the Mapping Class Group on Maximal Representations

Let Γ _g be the fundamental group of a closed oriented Riemann surface Σ _g , g ≥ 2, and let G be a simple Lie group of Hermitian type. The Toledo invariant defines the subset of maximal representations Rep_max(Γ _g , G) in the representation variety Rep(Γ _g , G). Rep_max(Γ _g , G) is a union of connected components with similar properties as Teichmüller space . We prove that the mapping class group acts properly on Rep_max(Γ _g , G) when , SU(n,n), SO*(4n), Spin(2,n).     

Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions

In this paper we develop a robust uncertainty principle for finite signals in which states that, for nearly all choices such that

Uncertainty Principles for Sturm–Liouville Operators

An uncertainty principle for the Sturm--Liouville operator $$ L=\frac{d^2}{dt^2}+a(t)\frac{d}{dt} $$ is established, as generalization of an inequality for Jacobi expansions proved in our previous paper, which implies the uncertainty principle for ultraspherical expansions by M. Rösler and M. Voit. The properties of the orthogonal set of eigenfunctions of the operator L and the so-called conjugate orthogonal set are unified by introducing the differential–difference operators, which are essential in our study. As consequences, an uncertainty principle for Laguerre, Hermite, and generalized Hermite expansions is obtained, respectively.     

广义baby TKK代数一类boson表示

利用文[3]中的结论构造群代数与对称代数在文[4]的基础上给出了广义baby TKK代数G(~T)的一类boson场表示.     

Inequalities and Local Uncertainty Principles for Nilpotent Lie Groups

Mathematical Notes - Let $$\mathbb{F}_{q}$$ be a finite field, let $$\mathbb{X}$$ be a subset of the projective space ?s?1 over $$\mathbb{F}_{q}$$ parametrized by rational functions,...     

一类分块矩阵群逆的表达式

鉴于分块矩阵的群逆在许多领域都有重要的应用,根据矩阵投影性质和初等分解的方法给出了分块矩阵M=(AX+YB AB D)在一些新的条件下群逆的存在性理论,然后根据群逆存在性的理论给出群逆的具体表达式.最后通过数值例子验证了结果的正确性.