On the structure of the space of wavelet transforms

Super-Wavelets Versus Poly-Bergman Spaces

“…See the papers [2][3][4]9]. It has also been motivated by the study of spaces of wavelet transform using restriction principles [11,12]. In the short note [1] we have constructed discrete versions (frames) of our wavelet transforms.…”

Wavelets from Laguerre Polynomials and Toeplitz-Type Operators

“…Following this scheme the next result gives the form of the Wick symbol of Calderón-Toeplitz operator T (k) a depending on v = ℑζ. Note that writing the Calderón-Toeplitz operator T (k) a in terms of its Wick symbol yields exactly the spectral-type representation (9). Recall that κ k is the constant depending on k given in (4).…”

“…The structure of the space of wavelet transforms inside L 2 (G, dν) (the space of all square-integrable functions on the affine group G with respect to the left invariant Haar measure dν) was described in our paper [9]. The key tool in this description is the (Bargmann-type) transform giving an isometrical isomorphism of the space L 2 (G, dν) under which the space of wavelet transforms is mapped onto tensor product of L 2 -spaces where one of them is the rank-one space generated by a suitable function.…”

On Boundedness of Calderón–Toeplitz Operators

“…Further each a n (v) can be uniformly approximated by smooth symbols, and thus belongs to the C * -algebra generated by Calderón-Toeplitz operators with smooth bounded symbols. According to Theorem 2.4 the Calderón-Toeplitz operator T (k) a acting on A (k) is unitarily equivalent to the multiplication operator γ a,k I acting on L 2 (R + ), where the function γ a,k is given by (6). Thus,…”

“…In [6] we have described the structure of the space of Calderón transforms W ψ (L 2 (R)) inside L 2 (R × R + , v −2 du dv). This representation was further used to study Calderón-Toeplitz operators acting on spaces of Calderón transforms for general (admissible) wavelets in [7].…”