Book Review: Functions with disconnected spectrum: Sampling, interpolation, translates
نویسندگان
چکیده
منابع مشابه
Spectrum of Fractal Interpolation Functions
where (x, y) ∈ S. The effects of an affine transform on a set are depicted in fig. 1. The union of N affine transformations is called the Hutchinson operator: W = ⋃N n=1 wn. For a specified metric the distance h(A, B) between two sets A, B can be defined. Under certain conditions [2] the Hutchinson operator is contractive, h(W (A),W (B)) ≤ sh(A, B), s < 1. Successive iterations with Hutchinson ...
متن کاملSampling Theory for Functions with Fractal Spectrum
CONTENTS We investigate in greater detail a sampling formula given by the 1 . Introduction fjrst author for functions whose spectrum lies in a Cantor set K of 2. Asymptotic Behavior of the Sampling Function a special type introduced by Jorgensen and Pedersen, where the 3. Translates of the Sampling Function sampling set is extremely thin, and the sampling function is quite 4. The Sampling Formu...
متن کاملInterpolation by Translates of a Basis Function
Interpolation using radial basis functions has become an established and useful technique in multi-dimensional data tting. It is a special case of interpolation by translates of a basis function. All the methods used in practice have a strong connection with a variational principle. In this paper we provide a straightforward approach to the variational principle, and make some useful practical ...
متن کاملSampling and Interpolation in Bargmann-fock Spaces of Polyanalytic Functions
We give a complete characterization of all lattice sampling and interpolating sequences in the Fock space of polyanalytic functions (polyFock spaces), displaying a ”Nyquist rate” which increases with the degree of polyanaliticity. This is done introducing a unitary mapping between vector valued Hilbert spaces and poly-Fock spaces. This mapping extends Bargmann ́s theory to polyanalytic spaces. T...
متن کاملOn Interpolation and Sampling in Hilbert Spaces of Analytic Functions
In this paper we give new proofs of some theorems due to Seip Seip Wallst en and Lyubarskii Seip on sequences of interpolation and sampling for spaces of analytic functions that are square integrable with respect to certain weights The results are also given in a somewhat more general setting Introduction In a series of recent papers Seip S Seip Wallst en S W and Lyuabarskii Seip L S have studi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2017
ISSN: 0273-0979,1088-9485
DOI: 10.1090/bull/1593