Search results for "Hilbert manifold"
showing 10 items of 10 documents
Hilbert Space Embeddings for Gelfand–Shilov and Pilipović Spaces
2017
We consider quasi-Banach spaces that lie between a Gelfand–Shilov space, or more generally, Pilipovi´c space, \(\mathcal{H}\), and its dual, \(\mathcal{H}^\prime\) . We prove that for such quasi-Banach space \(\mathcal{B}\), there are convenient Hilbert spaces, \(\mathcal{H}_{k}, k=1,2\), with normalized Hermite functions as orthonormal bases and such that \(\mathcal{B}\) lies between \(\mathcal{H}_1\; \mathrm{and}\;\mathcal{H}_2\), and the latter spaces lie between \(\mathcal{H}\; \mathrm{and}\;\mathcal{H}^\prime\).
QUASI *-ALGEBRAS OF OPERATORS AND THEIR APPLICATIONS
1995
The main facts of the theory of quasi*-algebras of operators acting in a rigged Hilbert space are reviewed. The particular case where the rigged Hilbert space is generated by a self-adjoint operator in Hilbert space is examined in more details. A series of applications to quantum theories are discussed.
Constructive proofs of representation theorems in separable Hilbert space
1964
Universal formulas for characteristic classes on the Hilbert schemes of points on surfaces
2007
This article can be seen as a sequel to the first author's article ``Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane'', where he calculates the total Chern class of the Hilbert schemes of points on the affine plane by proving a result on the existence of certain universal formulas expressing characteristic classes on the Hilbert schemes in term of Nakajima's creation operators. The purpose of this work is (at least) two-fold. First of all, we clarify the notion of ``universality'' of certain formulas about the cohomology of the Hilbert schemes by defining a universal algebra of creation operators. This helps us to reformulate and extend a lot of the f…
Rolle's Theorem for Polynomials of Degree Four in a Hilbert Space
2002
AbstractIn an infinite-dimensional real Hilbert space, we introduce a class of fourth-degree polynomials which do not satisfy Rolle's Theorem in the unit ball. Extending what happens in the finite-dimensional case, we show that every fourth-degree polynomial defined by a compact operator satisfies Rolle's Theorem.
Inversion Formulas for the Discretized Hilbert Transform on the Unit Circle
1998
A discrete version of the Hilbert transform on the unit circle is considered. Its Moore--Penrose inverse with respect to suitable scalar products is derived for different side conditions. Furthermore, stability of the pseudo-inverse is studied. These results allow the efficient computation of approximate solutions of singular integral equations with Hilbert kernel. Furthermore, the stability analysis of such methods becomes much easier even for graded meshes which are useful for weakly singular solutions.
Some results about operators in nested Hilbert spaces
2005
With the use of interpolation methods we obtain some results about the domain of an operator acting on the nested Hilbert space {ℋf}f∈∑ generated by a self-adjoint operatorA and some estimates of the norms of its representatives. Some consequences in the particular case of the scale of Hilbert spaces are discussed.
Stability of the fixed point property in Hilbert spaces
2005
In this paper we prove that if X X is a Banach space whose Banach-Mazur distance to a Hilbert space is less than 5 + 17 2 \sqrt {\frac {5+\sqrt {17}}{2}} , then X X has the fixed point property for nonexpansive mappings.