Iterative Reconstructions in Irregular Sampling With Derivatives
Frame Analysis of Irregular Periodic Sampling of Signals and Their Derivatives
Given a bandlimited signal, we consider the sampling of the signal and some of its derivatives in a periodic manner.
We deal with generalized Sobolev spaces WAk, where instead of requiring the functions and their derivatives to be in Ln/k, they are required to be in a rearrangement invariant space A which belongs to a certain class of spaces "close" to Ln/k.
Weighted Lq estimates for derivatives of weighted Hp functions
Aliasing error bounds are derived for one- and two-channel sampling series analogous to the Whittaker-Kotel'nikov-Shannon series, and for the multi-band sampling series, and a "derivative" extension of it, due to Dodson, Beaty, et al.
Examples are considered, and the frame bounds in the case of sampling of the signal and its first derivative are calculated explicitly.
This article also gives a single necessary-and-sufficient condition for a holomorphic function to be the transform of a function f such that any derivative of f multiplied by any polynomial is in Lp (d, ρ).
Applying a special derivative reproducing property, we show that when the kernel is real analytic, every function from the RKHS is real analytic.
5-Aza analogs were prepared of several tryptamine derivatives and a skatole derivative known to bind at human 5-HT6 receptors and evaluated to determine if they bind in a manner similar to their indolic analogs.
The kernel of a certain derivation of the polynomial ringk is shown to be nonfinitely generated overk (a field of charactersitic zero), thus giving a new counterexample to Hilbert's Fourteenth Problem.
These are analogous to "fusion rules" in tensor product decomposition and their derivation obtains from an analysis of theR-matrix.
A general method for a painless derivation of a dual pair of affine frames from an arbitrary MRA is obtained via the mixed extension principle.
We present here a self-contained derivation, building the decomposition from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering.
The derivation of our algorithm depends on certain properties of joint analyticity (with respect to spatial variables and perturbations) which had not been established before this work.