Sampling theorems and bases in a Hilbert space
نویسندگان
چکیده
منابع مشابه
Sampling Theorems and Bases in a Hilbert Space
A unified approach to sampling theorems for (wide sense) stat ionary random processes rests upon Hilbert space concepts. New results in sampling theory are obtained along the following lines: recovery of the process x(t) from nonperiodic samples, or when any finite number of samples are deleted; conditions for obtaining x (t) when only the past is sampled; a criterion for restoring x(t) from a ...
متن کاملSampling in a Hilbert Space
An analog of the Whittaker-Shannon-Kotel′nikov sampling theorem is derived for functions with values in a separable Hilbert space. The proof uses the concept of frames and frame operators in a Hilbert space. One of the consequences of this theorem is that it allows us to derive sampling theorems associated with boundary-value problems and some homogeneous integral equations, which in turn gives...
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An account of sampling in the setting of reproducing kernel spaces is given, the main point of which is to show that the sampling theory of Kluvánek, even though it is very general in some respects, is nevertheless a special case of the reproducing kernel theory. A Dictionary is provided as a handy summary of the essential steps. Starting with the classical formulation, the notion of band-limit...
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A sequence of vectors {f1, f2, f3, . . . } in a separable Hilbert space H is said to be a Schauder basis for H if every element f ∈ H has a unique norm-convergent expansion f = ∑ cnfn. If, in addition, there exist positive constants A and B such that A ∑ |cn| ≤ ∥∥∥∑ cnfn∥∥∥2 ≤ B∑ |cn|, then we call {f1, f2, f3, . . . } a Riesz basis. In the first half of this paper, we show that every Schauder ...
متن کاملOn duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules
In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...
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ژورنال
عنوان ژورنال: Information and Control
سال: 1961
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(61)80001-6