6,051 research outputs found
Representations for generalized Drazin inverse of operator matrices over a Banach space
In this paper we give expressions for the generalized Drazin inverse of a
(2,2,0) operator matrix and a operator matrix under certain
circumstances, which generalizes and unifies several results in the literature
The Weiss conjecture on admissibility of observation operators for contraction semigroups
We prove the conjecture of George Weiss for contraction semigroups on Hilbert spaces, giving a characterization of infinite-time admissible observation functionals for a contraction semigroup, namely that such a functional C is infinite-time admissible if and only if there is an M > 0 such that parallel to IC(sI - A)(-1)parallel to less than or equal to M/root Re s for all s in the open right half-plane. Here A denotes the infinitesimal generator of the semigroup. The result provides a simultaneous generalization of several celebrated results from the theory of Hardy spaces involving Carleson measures and Hankel operators
Exponential growth of colored HOMFLY-PT homology
We define reduced colored sl(N) link homologies and use deformation spectral
sequences to characterize their dependence on color and rank. We then define
reduced colored HOMFLY-PT homologies and prove that they arise as large N
limits of sl(N) homologies. Together, these results allow proofs of many
aspects of the physically conjectured structure of the family of type A link
homologies. In particular, we verify a conjecture of Gorsky, Gukov and
Sto\v{s}i\'c about the growth of colored HOMFLY-PT homologies.Comment: 39 pages, many figures. v2: version accepted for publication in
Advances in Mathematic
Bethe ansatz for the Ruijsenaars model of BC1- type
We consider one-dimensional elliptic Ruijsenaars model of type BC1. We show that when all coupling constants are integers, it has meromorphic eigenfunctions expressed by a variant of Bethe ansatz. This result generalizes the Bethe ansatz formulas known in the A1-case
The Freeness and Minimal Free Resolutions of Modules of Differential Operators of a Generic Hyperplane Arrangement
Let A be a generic hyperplane arrangement composed of r hyperplanes in an
n-dimensional vector space, and S the polynomial ring in n variables. We
consider the S-submodule D(m)(A) of the nth Weyl algebra of homogeneous
differential operators of order m preserving the defining ideal of A.
We prove that if n \geq 3, r > n,m > r - n + 1, then D(m)(A) is free (Holm's
conjecture). Combining this with some results by Holm, we see that D(m)(A) is
free unless n \geq 3, r > n,m < r - n + 1. In the remaining case, we construct
a minimal free resolution of D(m)(A) by generalizing Yuzvinsky's construction
for m = 1. In addition, we construct a minimal free resolution of the transpose
of the m-jet module, which generalizes a result by Rose and Terao for m = 1.Comment: 20 page
- …