Shift invariant spaces and prediction theory
نویسندگان
چکیده
منابع مشابه
Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups
We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...
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Given a frame for a subspace W of a Hilbert space H, we consider a class of oblique dual frame sequences. These dual frame sequences are not constrained to lie in W . Our main focus is on shift-invariant frame sequences of the form {φ(· − k)}k∈Z in subspaces of L2(R); for such frame sequences we are able to characterize the set of shift-invariant oblique dual Bessel sequences. Given frame seque...
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In this paper, we show that the property of tight affine frame decomposition of functions in L can be extended in a stable way to functions in Sobolev spaces when the generators of the tight affine frames satisfy certain mild regularity and vanishing moment conditions. Applying the affine frame operators Qj on j-th levels to any function f in a Sobolev space reveals the detailed information Qjf...
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In this paper we investigate the structure of finitely generated shift-invariant spaces and solvability of linear operator equations. Fourier transforms and semi-convolutions are used to characterize shift-invariant spaces. Criteria are provided for solvability of linear operator equations, including linear partial difference equations and discrete convolution equations. The results are then ap...
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A moduli space is a space that parametrizes geometric objects. For example, elliptic curves are classified by the so-called J-invariant, so the moduli space of elliptic curves is a line (with coordinate J). More generally, there exists a moduli space, calledMg , which parametries all projective algebraic curves of genus g (equivalently, all compact Riemann surfaces of genus g). The Jacobian of ...
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 1962
ISSN: 0001-5962
DOI: 10.1007/bf02545791