81 research outputs found
Factorizations of Kernels and Reproducing Kernel Hilbert Spaces
No full textIn this talk we will explain a series of results concerning reproducing kernel Hilbert spaces, related to the factorization of their kernels. In particular, we will talk about (trivial) isometric multipliers for a large class of reproducing kernel Hilbert spaces. We will then discuss a particular type of dilation, as well as a classification of Brehmer/Beurling type invariant subspaces of natural reproducing kernel Hilbert spaces. This is joint work with R. Kumari, S. Sarkar and D. Timotin
An invariant subspace theorem and invariant subspaces of analytic reproducing Kernel Hilbert Spaces - II
No full textThis paper is a follow-up contribution to our work (Sarkar in J Oper Theory, 73:433–441, 2015) where we discussed some invariant subspace results for contractions on Hilbert spaces. Here we extend the results of (Sarkar in J Oper Theory, 73:433–441, 2015) to the context of n-tuples of bounded linear operators on Hilbert spaces. Let T = (T1,…,Tn) be a pure commuting co-spherically contractive n-tuple of operators on a Hilbert space H and S be a non-trivial closed subspace of H. One of our main results states that: S is a joint T-invariant subspace if and only if there exists a partially isometric operator Π ∊B(H2n(ε),H) such that , S = ΠH2n(ε) where H2n is the Drury–Arveson space and ε is a coefficient Hilbert space and TiΠ = ΠMzi, i = 1,…,n. In particular, it follows that a shift invariant subspace of a “nice” reproducing kernel Hilbert space over the unit ball in Cn is the range of a “multiplier” with closed range. Our work addresses the case of joint shift invariant subspaces of the Hardy space and the weighted Bergman spaces over the unit ball in Cn
Use of Metallic Materials as Medium of Architectural Expression
No full textThe imagination and the thought of the architects backed by their creative urge find expression in architecture. A careful selection of building materials plays an important role in successful translation of architects' imagination as also in shaping the three dimensional form with req-uired aesthetic flavour. It has been possible to introduce a number of new materials in the sphere of building activ-ities, in addition to conventional natural ones, through a process of continuous research and development. The expl-oitation of a new material demands understanding & imag- ination otherwise, even under favourable circumstances its potential remain unused and unexplored
Wold decomposition for doubly commuting isometries
No full textIn this paper, we obtain a complete description of the class of n-tuples (n ≥ 2) of doubly commuting isometries. In particular, we present a several variables analogue of the Wold decomposition for isometries on Hilbert spaces. Our main result is a generalization of M. Slocinskiʼs Wold-type decomposition of a pair of doubly commuting isometries
Submodules of the Hardy module over the polydisc
No full textWe say that a submodule S of H2(Dn) (n > 1) is co-doubly commuting if the quotient module H2(n)/S is doubly commuting. We show that a co-doubly commuting submodule of H2(Dn) is essentially doubly commuting if and only if the corresponding one-variable inner functions are finite Blaschke products or n = 2. In particular, a co-doubly commuting submodule S of H2(Dn) is essentially doubly commuting if and only if n = 2 or that S is of finite co-dimension. We obtain an explicit representation of the Beurling–Lax–Halmos inner functions for those submodules of H2 H2(Dn-1)(D) which are co-doubly commuting submodules of H2(Dn). Finally, we prove that a pair of co-doubly commuting submodules of H2(Dn) are unitarily equivalent if and only if they are equal
Invariant and wandering subspaces of reproducing kernel Hilbert spaces
No full textNon UBCUnreviewedAuthor affiliation: Indian Statistical InstituteFacult
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