‎The proximal point algorithm‎, ‎which is a well-known tool for finding‎ ‎minima of convex functions‎, ‎is generalized from the classical‎ ‎Hilbert space framework into a nonlinear setting‎, ‎namely‎, ‎geodesic‎ ‎metric spaces of nonpositive curvature‎. ‎In this paper we propose an‎  ‎iterative algorithm for finding the common element of the‎ ‎minimizers of a finite family of convex functions a...

Abstract. We give a detailed description of the resolution of the identity of a second order q-difference operator considered as an unbounded self-adjoint operator on two different Hilbert spaces. The q-difference operator and the two choices of Hilbert spaces naturally arise from harmonic analysis on the quantum group SUq(1, 1) and SUq(2). The spectral analysis associated to SUq(1, 1) leads to...

We study the relationship between sampling sequences in infinite dimensional Hilbert spaces of analytic functions and Marcinkiewicz-Zygmund inequalities subspaces polynomials. focus on Hardy space Bergman one variable because they provide two settings with a strikingly different behavior.

We introduce a natural class of functions, the pseudomultipliers, associated with a general Hilbert function space, prove an extension theorem which justifies the definition, give numerous examples and establish the nature of the 1-pseudomultipliers of Hilbert spaces of analytic functions under mild hypotheses. The function 1/z on the unit disc D is almost a multiplier of the Hardy space H: it ...

In this note we study some basic properties of the γinterpolation method introduced in [6] e.g. interpolation of Bochner spaces and interpolation of analytic operator valued functions in the sense of Stein. As applications we consider the interpolation of almost summing operators (in particular γ-radonifying and Hilbert-Schmidt operators) and of γ-Sobolev spaces as introduced in [6]. We also co...

in this paper some new applications of empirical mode decomposition (emd) and hilbert spectrum in seismic ground-roll attenuation, random noise attenuation and spectral decomposition are introduced. hilbert spectrum is a time-frequency representation for hilbert-huang transform which is obtained by combination of instantaneous frequency (if) concept and intrinsic mode function of empirical mode...

In the study of Hilbert spaces of analytic functions, it is noticed that complete interpolating sequences and Riesz bases of reproducing kernels are dual notions. In this work we make this duality explicit by identifying sequences of complex numbers with linear operators.