منابع مشابه
Sampling Theorems for Multivariate Shift Invariant Subspaces ∗
Regular and irregular sampling theorems for multivariate shift invariant subspaces are studied. We give a characterization of regular points and an irregular sampling theorem, which covers many known results, e.g., Kadec’s 1/4-theorem. We show that some subspaces may not have a regular point. We also present a reconstruction algorithm which is slightly different from the known one but is more e...
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We define the local trace function for subspaces of L (Rn) which are invariant under integer translation. Our trace function contains the dimension function and the spectral function defined in [BoRz] and completely characterizes the given translation invariant subspace. It has properties such as positivity, additivity, monotony and some form of continuity. It behaves nicely under dilations and...
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In this paper we study extremal functions for invariant subspaces Ji of the Dirichlet shift, i.e., solutions <p of the extremal problem »up{|/"»(0)|/||/||fl:/eur, /VO}. Here n is the smallest nonnegative integer such that the sup is positive. It is known that such a function <p generates J! . We show that the derivative (zip)' has a pseudocontinuation to the exterior disc. This pseudocontinuati...
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By a famous result, functions in backward shift invariant subspaces in Hardy spaces are characterized by the fact that they admit a pseudocontinuation a.e. on T. More can be said if the spectrum of the associated inner function has holes on T. Then the functions of the invariant subspaces even extend analytically through these holes. We will discuss the situation in weighted backward shift inva...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2002
ISSN: 0021-9045
DOI: 10.1006/jath.2002.3711