The wavelet dimension function for arbitrary real dilations is defined and used to address several questions involving the existence of MRA wavelets and well-localized wavelets for irrational dilations. The theory of quasi-affine frames for rational dilations and the existence of non-MSF wavelets for certain irrational dilations play an important role in this development. Expansive dilations ad...

let denote the unit circle in the complex plane. given a function , one uses t usual (harmonic) poisson kernel for the unit disk to define the poisson integral of , namely . here we consider the biharmonic poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . we then consider the dilations for and . the ...

The effects of stimulating P2Y1 or P2Y2 purinoceptors on the endothelium of isolated middle cerebral arteries (MCAs), third-order branches of the MCA (bMCAs), and penetrating arterioles (PAs) of the rat were studied. After pressurization and development of spontaneous tone (25% contraction), resting diameters for MCAs, bMCAs, and PAs were 203 ± 5 ( n = 50), 99 ± 2 ( n = 42), and 87 ± 2 μm ( n =...

Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...