Search results for "Intertwining operator"
showing 4 items of 4 documents
Intertwining operators between different Hilbert spaces: connection with frames
2009
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral self-adjoint operators living in different Hilbert spaces. Many examples are discussed in details. Many of them arise from the theory of frames in Hilbert spaces, others from the so-called g-frames.
Quons, coherent states and intertwining operators
2009
We propose a differential representation for the operators satisfying the q-mutation relation $BB^\dagger-q B^\dagger B=\1$ which generalizes a recent result by Eremin and Meldianov, and we discuss in detail this choice in the limit $q\to1$. Further, we build up non-linear and Gazeau-Klauder coherent states associated to the free quonic hamiltonian $h_1=B^\dagger B$. Finally we construct almost isospectrals quonic hamiltonians adopting the results on intertwining operators recently proposed by the author.
Vector coherent states and intertwining operators
2009
In this paper we discuss a general strategy to construct vector coherent states of the Gazeau-Klauder type and we use them to built up examples of isospectral hamiltonians. For that we use a general strategy recently proposed by the author and which extends well known facts on intertwining operators. We also discuss the possibility of constructing non-isospectral hamiltonians with related eigenstates.
Mathematical aspects of intertwining operators: the role of Riesz bases
2010
In this paper we continue our analysis of intertwining relations for both self-adjoint and not self-adjoint operators. In particular, in this last situation, we discuss the connection with pseudo-hermitian quantum mechanics and the role of Riesz bases.