Title of article :
Random sampling in shift invariant spaces
Author/Authors :
Yang، نويسنده , , Jianbin and Wei، نويسنده , , Wei، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2013
Pages :
9
From page :
26
To page :
34
Abstract :
The set of sampling in a shift invariant space plays an important role in signal processing and has many applications. This paper addresses the problem when some randomly chosen samples X = { x j : j ∈ J } form a set of sampling in a shift invariant space. That is, when the inequality of the form c p ‖ f ‖ L p ( R d ) p ≤ ∑ x j ∈ X | f ( x j ) | p ≤ C p ‖ f ‖ L p ( R d ) p holds uniformly for all functions f in a shift invariant space, where c p and C p are positive constants ( 1 ≤ p ≤ ∞ ) . We prove that with overwhelming probability, the above sampling inequality holds for certain compact subsets of the shift invariant space when the sampling size is sufficiently large.
Keywords :
Covering number , Shift invariant spaces , Random sampling
Journal title :
Journal of Mathematical Analysis and Applications
Serial Year :
2013
Journal title :
Journal of Mathematical Analysis and Applications
Record number :
1563201
Link To Document :
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