Related papers: Triplets of Closely Embedded Hilbert Spaces
We use a model operator approach and the spectral theorem for self-adjoint operators in a Hilbert space to derive the basic results of abstract left-definite theory in a straightforward manner. The theory is amply illustrated with a variety…
Most research into similarity search in metric spaces relies upon the triangle inequality property. This property allows the space to be arranged according to relative distances to avoid searching some subspaces. We show that many common…
We obtain solutions of the Wheeler-DeWitt equation with positive cosmological constant for a closed universe in the large-volume limit. We argue that this space of solutions provides a complete basis for the Hilbert space of quantum gravity…
In this paper, we introduce and study the class of {\it enriched strictly pseudocontractive mappings} in Hilbert spaces and extend the corresponding convergence theorem (Theorem 12) in [Browder, F. E., Petryshyn, W. V., {\it Construction of…
We expand the basic geometric elements of the simplex method to linear programs in locally convex topological vector spaces and provide conditions under which the method converges in value to optimality. This setting generalizes many…
The hyperinvariant subspace problem is solved in the setting of Hilbert and right Hamilton space, motivated by my earlier works in the invariant subspace problem.
It is shown that the natural framework for the solutions of any Schrodinger equation whose spectrum has a continuous part is the Rigged Hilbert Space rather than just the Hilbert space. The difficulties of using only the Hilbert space to…
We treat the boundary problem for complex varieties with isolated singularities, of complex dimension greater than or equal to 3, non necessarily compact, which are contained in strongly convex, open subsets of a complex Hilbert space H. We…
This series of papers is devoted to an open-ended project aimed at the solution of Hilbert's sixth problem (concerning joint axiomatization of physics and probability theory) proposed to be constructed in the framework of an all-embracing…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Semi-cosimplicial objects in the category of Hilbert spaces with isometries which are motivated by non-commutative probability theory, in particular by the distributional symmetry of spreadability, are introduced and systematically…
We develop the theory of $J$-holomorphic discs in Hilbert spaces with almost complex structures. As an aplication, we prove a version of Gromov's symplectic non-squeezing theorem for Hilbert spaces. It can be applied to short-time…
The solution of constrained linear partial-differential equations can be described via parametric representations of linear relations. To study these representations, we provide a novel definition of boundary triplets for linear relations…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…
We study de Sitter JT gravity in the canonical formulation to illustrate constructions of Hilbert spaces in quantum gravity, which is challenging due to the Hamiltonian constraints. The key ideas include representing states as "invariants"…
In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in…
This monograph is centred at the intersection of three mathematical topics, that are theoretical in nature, yet with motivations and relevance deep rooted in applications: the linear inverse problems on abstract, in general…
The results in the paper are related to the classification problem for invariant subspaces of multiplication operators in several variables. The main results consist of characterizations, in the two dimensional case, of ideals of…
In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…
We study Hilbert spaces $H$ interpreted, in an appropriate sense, in a first-order theory. Under a new finiteness hypothesis that we call {\em scatteredness} we prove that $H$ is a direct sum of {\em asymptotically free} components, where…