Related papers: Hadamard's lemma in separable Hilbert spaces
In this paper, we study the Hilbert$-$Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
There are significant differences between Helmholtz and Hodge's decomposition theorems, but both share a common flavor. This paper is a first step to bring them together. We here produce Helmholtz theorems for differential 1-forms and…
This paper is devoted to a generalization of a Hadamard type inequality for the permanent of a complex square matrix. Our proof is based on a non-trivial extension of a technique used in Carlen, Lieb and Loss (Methods and Applications of…
We extend the Fuglede-Putnam theorem from the algebra $B(H)$ of all bounded operators on the Hilbert space $H$ to the algebra of all locally measurable operators affiliated with a von Neumann algebra.
For a finite lattice $\Lambda$, $\Lambda$-ultrametric spaces have, among other reasons, appeared as a means of constructing structures with lattices of equivalence relations embedding $\Lambda$. This makes use of an isomorphism of…
We generalize the classical de Rham decomposition theorem for Riemannian manifolds to the setting of geodesic metric spaces of finite dimension.
We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for $U$-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued $U$-statistics of…
A general solution to the Complex Bateman equation in a space of arbitrary dimensions is constructed.
Extending the concept of frame to continuous frame, in this manuscript we will show that under certain conditions on the measure of $\Omega$ and the dimension of $\h$ we can construct continuous frames. Also, some examples are given.
We present a concise proof for the supporting hyperplane theorem. We then observe that the proof not only establishes the supporting hyperplane theorem but also extends it to a hyperplane separation theorem for certain non-convex sets. The…
We give necessary conditions for a set E to be removable for Holder continuous quasiregular mappings in the plane. We also obtain some removability results for Holder continuous mappings of finite distortion.
We formulate and prove a general result in spirit of hypergraph removal lemma for measurable functions of several variables.
We prove the extended Hilbert's Nullstellensatz in the context of Hu-Liu polynomial trirings.
We discuss the possibility of introducing a multi-resolution in a Hilbert space which is not necessarily a space of functions. We investigate which of the classical properties can be translated to this more general framework and the way in…
A useful result is that if a bounded complex-valued path is Riemann-integrable, then its modulus is also Riemann-integrable. The extension of this last result to bounded paths taking values in a normed space is affirmed, as being true, in…
In this paper, we will solve the Reifenberg Plateau Problem in Hilbert space.
We present a new discretization for the Hadamard fractional derivative, that simplifies the computations. We then apply the method to solve a fractional differential equation and a fractional variational problem with dependence on the…
The Hilbert metric on convex subsets of $\mathbb R^n$ has proven a rich notion and has been extensively studied. We propose here a generalization of this metric to subset of complex projective spaces and give examples of applications to…
We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…