Search results for "Hadamard product"
showing 7 items of 7 documents
Algebras of frequently hypercyclic vectors
2019
We show that the multiples of the backward shift operator on the spaces $\ell_{p}$, $1\leq p<\infty$, or $c_{0}$, when endowed with coordinatewise multiplication, do not possess frequently hypercyclic algebras. More generally, we characterize the existence of algebras of $\mathcal{A}$-hypercyclic vectors for these operators. We also show that the differentiation operator on the space of entire functions, when endowed with the Hadamard product, does not possess frequently hypercyclic algebras. On the other hand, we show that for any frequently hypercyclic operator $T$ on any Banach space, $FHC(T)$ is algebrable for a suitable product, and in some cases it is even strongly algebrable.
Method specific Cholesky decomposition : Coulomb and exchange energies
2008
We present a novel approach to the calculation of the Coulomb and exchange contributions to the total electronic energy in self consistent field and density functional theory. The numerical procedure is based on the Cholesky decomposition and involves decomposition of specific Hadamard product matrices that enter the energy expression. In this way, we determine an auxiliary basis and obtain a dramatic reduction in size as compared to the resolution of identity (RI) method. Although the auxiliary basis is determined from the energy expression, we have complete control of the errors in the gradient or Fock matrix. Another important advantage of this method specific Cholesky decomposition is t…
Some fourth order CY-type operators with non symplectically rigid monodromy
2012
We study tuples of matrices with rigidity index two in $\Sp_4(\mathbb{C})$, which are potentially induced by differential operators of Calabi-Yau type. The constructions of those monodromy tuples via algebraic operations and middle convolutions and the related constructions on the level differential operators lead to previously known and new examples.
Vector-valued sequences and multipliers
2015
El texto que se presenta trata de establecer un marco teórico en el que poder manejar dos nuevos conceptos (extensión de conceptos ya conocidos): los multiplicadores por coeficientes a través de una aplicación bilineal y el producto proyectivo tensorial de Hadamard. Ambos espacios se ven siempre como espacios de sucesiones a valores vectoriales, esto es, en un espacio de Banach cualquiera. Posteriormente, se estudia la relación entre ellos y se aportan algunos ejemplos. El punto de partida del proyecto son las clases de espacios introducidas por O.Blasco y M. Pavlovic en el trabajo "Coefficient multipliers on spaces of analytic functions" (Revista Mat. Iberoamericana, 2011) donde se formali…
Rational normal curves and Hadamard products
2021
AbstractGiven $$r>n$$ r > n general hyperplanes in $$\mathbb P^n,$$ P n , a star configuration of points is the set of all the n-wise intersection of the hyperplanes. We introduce contact star configurations, which are star configurations where all the hyperplanes are osculating to the same rational normal curve. In this paper, we find a relation between this construction and Hadamard products of linear varieties. Moreover, we study the union of contact star configurations on a same conic in $$\mathbb P^2$$ P 2 , we prove that the union of two contact star configurations has a special h-vector and, in some cases, this is a complete intersection.
New spaces of matrices with operator entries
2019
In this paper, we will consider matrices with entries in the space of operators $\mathcal{B}(H)$, where $H$ is a separable Hilbert space and consider the class of matrices that can be approached in the operator norm by matrices with a finite number of diagonals. We will use the Schur product with Toeplitz matrices generated by summability kernels to describe such a class and show that in the case of Toeplitz matrices it can be identified with the space of continuous functions with values in $\mathcal B(H)$. We shall also introduce matriceal versions with operator entries of classical spaces of holomorphic functions such as $H^\infty(\mathbb{D})$ and $A(\mathbb{D})$ when dealing with upper t…
On symplectically rigid local systems of rank four and Calabi–Yau operators
2013
AbstractWe classify all Sp4(C)-rigid, quasi-unipotent local systems and show that all of them have geometric origin. Furthermore, we investigate which of those having a maximal unipotent element are induced by fourth order Calabi–Yau operators. Via this approach, we reconstruct all known Calabi–Yau operators inducing an Sp4(C)-rigid monodromy tuple and obtain closed formulae for special solutions of them.