Let H be a reproducing kernel Hilbert space of functions on set X . We study the problem finding minimal geodesic Grassmann manifold that joins two subspaces consisting which vanish given finite subsets establish necessary and sufficient condition for existence uniqueness geodesics, we then analyze it in examples. discuss relation distance with other known metrics when mentioned are singletons....

The role of Liouville operators in the study dynamical systems through use occupation measures has been an active area research control theory over past decade. This manuscript investigates Hardy space, which encode complex ordinary differential equations operator a reproducing kernel Hilbert space.

A discrete Hardy-type inequality ( ∑∞ n=1( ∑n k=1dn,kak)un) ≤ C( ∑∞ n=1 a p nvn) is considered for a positive “kernel” d = {dn,k}, n,k ∈ Z+, and p ≤ q. For kernels of product type some scales of weight characterizations of the inequality are proved with the corresponding estimates of the best constant C. A sufficient condition for the inequality to hold in the general case is proved and this co...

We treat the complex harmonic function on the Np–ball which is defined by the Np–norm related to the Lie norm. As a subspace, we treat Hardy spaces and consider the Bergman kernel on those spaces. Then, we try to construct the Bergman kernel in a concrete form in 2–dimensional Euclidean space. Introduction. In [2], [4], [6] and [7], we studied holomorphic functions and analytic functionals on t...

entropy as a measure of uncertainty was used to represent the results of the wavelet technique in electrochemical noise analysis. the experimental signals were obtained by recording the electrochemical potential and current noise of 7075 aluminum alloy in 3.5% nacl solution. the electrochemical potential and current noise were decomposed into 16 levels using daubechies wavelets. wavelet output ...

Maximal and atomic Hardy spaces Hp and H A, 0 < p ≤ 1, are considered in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. It is shown that Hp = H A with equivalent norms.