By studying the spectral aspects of fractional part function in a well-known separable Hilbert space, we show, among other things, rational approximation Riemann zeta and its derivatives valid on every vertical line right half-planes $\Re s> 1/2$ s >0.$ Moreover, provide some discussions explicit computations related to function.

We establish a regular sampling theory in the range of analysis operator continuous frame having unitary structure. The structure is related with representation locally compact abelian group on separable Hilbert space. samples are defined by means suitable discrete convolution systems which generalize some usual settings; here that taken at countable subgroup.

In [1], by using Fredholm index we developed a version of Quillen’s geometric cobordism theory for infinite dimensional Hilbert manifolds. This cobordism theory has a graded group structure under topological union operation and has push-forward maps for complex orientable Fredholm maps. In [19], by using Quinn’s Transversality Theorem [23], it has been shown that this cobordism theory has a gra...

Let H be an infinite-dimensional real separable Hilbert space. Given an unknown mapping M :H (r)H that can only be observed with noise, we consider two modified Robbins-Monro procedures to estimate the zero point ?o ( H of M. These procedures work in appropriate finite dimensional sub-spaces of growing dimension. Almost-sure convergence, functional central limit theorem (hence asymptotic normal...

We consider a probability measure m on a Hilbert space X and a bounded linear transformation on X that preserves the measure. We characterize the linear dynamical systems (X, m, T) for the cases where either X is finite dimensional or T is unitary and we give an example where T is a weighted shift operator. We apply the results to the limit identification problem for a vector-valued ergodic the...

in a real separable Hilbert space H , where the linear (possibly multivalued) operator A : D(A) ⊂H →H is the infinitesimal generator of a strongly continuous cosine family on H , W is a K-valued Wiener process with incremental covariance given by the nuclear operator Q defined on a complete probability space (Ω, ,P) equipped with a normal filtration ( t)t≥0, φ ∈ L(Ω;Cr), and σ is an 0-measurabl...

Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of ...

In this work, we use similarly separable vectors in Hilbert spaces to provide generalized integral results related majorization, Niezgoda, and Ćebysév type inequalities. Next, furnish some refinements of these Theorems obtained work extend improve several known the literature. An important aspect our is that inequalities are directly Arithmetic, Geometric, Harmonic, Power means. These means hav...