Related papers: Wirtinger's Calculus in general Hilbert Spaces
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
We undertake herein to derive the Wigner-Wilkins [W-W] neutron/nucleus scattering kernel, a foundation stone in neutron thermalization theory, on the basis of a self-contained calculation in quantum mechanics. Indeed, a quantum-mechanical…
The aim of this work is the study of the Weinstein $L^2$- multiplier operators on $\mathbb{R}^{d+1}_+$ and we give for them Calder\'on's reproducing formulas and best approximation using the theory of Weinstein transform and reproducing…
In this paper we investigate the reproducing kernel Hilbert space where the polylogarithm appears as kernel functions. This investigation begins with the properties of functions in this space, and here a connection to the classical Hardy…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
We determine the best n-term approximation of generalized Wiener model classes in a Hilbert space $H $. This theory is then applied to several special cases.
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
Although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications such as communications. In this work, we…
In this article, we prove an inner product inequality for Hilbert space operators. This inequality, then, is utilized to present a general numerical radius inequality using convex functions. Applications of the new results include obtaining…
We propose a new viewpoint on Hilbert scales extending them by means of all Hilbert spaces that are interpolation ones between spaces on the scale. We prove that this extension admits an explicit description with the help of…
We consider a certain Hartogs domain which is related to the Fock-Bargmann space. We give an explicit formula for the Bergman kernel of the domain in terms of the polylogarithm functions. Moreover we solve the Lu Qi-Keng problem of the…
In this article we discuss a generalized Wirtinger inequality.
Based on the local fractional calculus, we establish some new generalizations of H\"{o}lder's inequality. By using it, some results on the generalized integral inequality in fractal space are investigated in detail.
The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
We prove a Hankel-variant commutant lifting theorem. This also uncovers the complete structure of the Beurling-type reducing and invariant subspaces of Hankel operators. Kernel spaces of Hankel operators play a key role in the analysis.
We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…
The neural tangent kernel is a kernel function defined over the parameter distribution of an infinite width neural network. Despite the impracticality of this limit, the neural tangent kernel has allowed for a more direct study of neural…
General fractional calculus offers an elegant and self-consistent path toward the generalization of fractional calculus to an enhanced class of kernels. Prabhakar's theory can be thought of, to some extent, as an explicit realization of…
In this paper, we characterize Probabilistic Principal Component Analysis in Hilbert spaces and demonstrate how the optimal solution admits a representation in dual space. This allows us to develop a generative framework for kernel methods.…