Classic hypercomplex analysis is intimately linked with elliptic operators, such as the Laplacian or Dirac operator, and positive quadratic forms. But there are many applications like crystallographic X-ray transform ultrahyperbolic operator which closely connected indefinite Although appearing in papers cases Hilbert modules not right choice function spaces since they do reflect induced geomet...

In this paper, by using some classical Mulholland type inequality, Berezin symbols and reproducing kernel technique, we prove the power inequalities for number $ber(A)$ self-adjoint operators $A$ on ${H}(\Omega )$. Namely, inequality Hilbert space are established. By applying that $(ber(A))^{n}\leq C_{1}ber(A^{n})$ any positive operator

Description: Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and explaining when and why these spaces are efficacious. The novel viewpoint is that reproducing kernel Hilbert space theory studies extrinsic geome...

Reproducing kernel Hilbert spaces and wavelets are both mathematical tools used in system identification and approximation. Reproducing kernel Hilbert spaces are function spaces possessing special characteristics that facilitate the search for solutions to norm minimization problems [3]. As such, they are of interest in a variety of areas including Machine Learning [11]. Wavelets are another mo...

We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by kernels whose dual systems form molecules, ensuring the size profile of a function is fully reflected its sampled values. The main tool local holomorphic calculus for convolution-dominated operators, valid groups with possibly non-polynomial growth. Applied to matrix coefficients group repres...