An isomorphic mapping is built between Hibert space L2 [0,1 j and reproducing kernel space H1 [ 0,1 ] using integral operator while wavelet approximation expressions and sampling expressions in the H1 [0,1 j are discussed as well.
First we show that the representation ofG×G on eachG-biinvariant irreducible reproducing kernel Hilbert space in Hol(D) is a highest weight representation whose kernel is the character of a highest weight representation ofG.
We show that every frame for a Hilbert space H can be written as a (multiple of a) sum of three orthonormal bases for H.
Finally, every frame can be written as a (multiple of a) average of two orthonormal bases for a larger Hilbert space.
Let Ω ??d have finite positive Lebesgue measure, and let (Ω) be the corresponding Hilbert space of-functions on Ω.
A frame in a Hilbert space allows every element in to be written as a linear combination of the frame elements, with coefficients called frame coefficients.
The present paper deals with dual theorem, functinal calculus, restriction and quotient operators; In particular, for Hilbert spaces, or L-spaces, it is proved that a n-tuple of commuting operators is spectral iff the operators in the n-tuple of commuting operators are spectral operators.