ISSN:
1531-5851
Keywords:
Primary 30D15
;
42C15
;
Secondary 30D10
;
42C30
;
Paley-Wiener space
;
entire functions of exponential type
;
exponential frames
;
discrete norms
;
sampling theorem
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract It is well known that for certain sequences {tn}n∈ℤ the usual Lp norm ∥·∥p in the Paley-Wiener space PW τ p is equivalent to the discrete norm ‖f‖p,{tn}:=(∑ n=−∞ ∞ |f(tn)|p)1/p for 1 ≤ p = 〈 ∞ and ‖f‖∞,{tn}:=sup n∈ℤ|f(tn| for p=∞). We estimate ∥f∥p from above by C∥f∥p, n and give an explicit value for C depending only on p, τ, and characteristic parameters of the sequence {tn}n∈ℤ. This includes an explicit lower frame bound in a famous theorem of Duffin and Schaeffer.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01261609
Permalink
