Operators Commuting with a Discrete Subgroup of Translations

نویسنده

  • H. G. FEICHTINGER
چکیده

We study the structure of operators from the Schwartz space S (R) into the tempered distributions S (R) that commute with a discrete subgroup of translations. The formalism leads to simple derivations of recent results about the frame operator of shift-invariant systems, Gabor and wavelet frames.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Spectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+

We study the spectrum of multipliers (bounded operators commuting with the shift operator S) on a Banach space E of sequences on Z. Given a multiplier M , we prove that f M(σ(S)) ⊂ σ(M) where f M is the symbol of M . We obtain a similar result for the spectrum of an operator commuting with the shift on a Banach space of sequences on Z. We generalize the results for multipliers on Banach spaces ...

متن کامل

Evolution Operators for Quantum Chains

Discrete-time evolution operators in integrable quantum lattice models are sometimes more fundamental objects then Hamiltonians. In this paper we study an evolution operator for the one-dimensional integrable q-deformed Bose gas with XXZ-type impurities and find its spectrum. Evolution operators give a new interpretation of known integrable systems, for instance our system describes apparently ...

متن کامل

Relative n-th non-commuting graphs of finite groups

‎Suppose $n$ is a fixed positive integer‎. ‎We introduce the relative n-th non-commuting graph $Gamma^{n} _{H,G}$‎, ‎associated to the non-abelian subgroup $H$ of group $G$‎. ‎The vertex set is $Gsetminus C^n_{H,G}$ in which $C^n_{H,G} = {xin G‎ : ‎[x,y^{n}]=1 mbox{~and~} [x^{n},y]=1mbox{~for~all~} yin H}$‎. ‎Moreover‎, ‎${x,y}$ is an edge if $x$ or $y$ belong to $H$ and $xy^{n}eq y^{n}x$ or $x...

متن کامل

Localization of Massless Spinning Particles and the Berry Phase

The components of the position operator, at a fixed time, for a massless and spinning particle with given helicity λ described in terms of bosonic degrees of freedom have an anomalous commutator proportional to λ. The position operator generates translations in momentum space. We show that a ray-representation for these translations emerges due to the non-commuting components of the position op...

متن کامل

The Sums and Products of Commuting AC-Operators

Abstract: In this paper, we exhibit new conditions for the sum of two commuting AC-operators to be again an AC-operator. In particular, this is satisfied on Hilbert space when one of them is a scalar-type spectral operator.  

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005