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There is a generalized oscillator algebra associated with every class of orthogonal polynomials {Ψn(x)}n=0∞, on the real line, satisfying a three term recurrence relation xΨn(x) = bnΨn+1(x) +… (More)

Coherent states, similar to the canonical coherent states of the harmonic oscillator, labeled by quaternions are established on the right and left quaternionic Hilbert spaces. On the left… (More)

Using the orthonormality of the 2D-Zernike polynomials, reproducing kernels, reproducing kernel Hilbert spaces, and ensuring coherent states attained. With the aid of the so-obtained coherent states,… (More)

In this thesis we develop vector coherent states (VCS) in the form [Special characters omitted.] where [Special characters omitted.] , the n dimensional complex space and [Special characters… (More)

In this note, following the theory of discrete frame perturbations in a complex Hilbert space, we examine perturbation of rank $n$ continuous frame, rank $n$ continuous Bessel family and rank $n$… (More)

Eigenfunctions and eigenvalues of the free magnetic Schrodinger operator, describing a spinless particle confined to an infinite layer of fixed width, are discussed in detail. The eigenfunctions are… (More)

A general theory of reproducing kernels and reproducing kernel Hilbert spaces on a right quaternionic Hilbert space is presented. Positive operator-valued measures and their connection to a class of… (More)

The canonical coherent states were labeled by a single complex number z. In this article we present classes of coherent states labeled by some other choices, namely the iterates of a complex… (More)

We present a class of vector coherent states in the domain $D\times D\times >....\times D$ (n-copies), where $D$ is the complex unit disc, using a specific class of hermitian matrices. Further, as an… (More)