In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are  generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.

The basic mathematical framework for super Hilbert spaces over a Graßmann algebra with a Graßmann number-valued inner product is formulated. Super Hilbert spaces over infinitely generated Graßmann algebras arise in the functional Schrödinger representation of spinor quantum field theory in a natural way. a email: [email protected]

In this paper, we first introduce a class of nonlinear mappings called extended hybrid in a Hilbert space containing the class of generalized hybrid mappings. The class is different from the class of super hybrid mappings which was defined by Kocourek, Takahashi and Yao [12]. We prove a fixed point theorem for generalized hybrid nonself-mapping in a Hilbert space. Next, we prove a nonlinear erg...

The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system ...

The super-Macdonald polynomials, introduced by Sergeev and Veselov, generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, they are eigenfunctions deformed Macdonald-Ruijsenaars operators same authors. We introduce a Hermitian form on algebra spanned prove their orthogonality, compute (quadratic) norms explicitly, establish corresponding Hilbert space interpretat...

A superqubit, belonging to a (2|1)-dimensional super-Hilbert space, constitutes the minimal supersymmetric extension of the conventional qubit. In order to see whether superqubits are more non-local than ordinary qubits, we construct a class of two-superqubit entangled states as a non-local resource in the CHSH game. Since super Hilbert space amplitudes are Grassmann numbers, the result depends...

Tikhonov regularization approach and block motion model are used to solve super-resolution problem for face video data. Video is preprocessed by 2-D empirical mode decomposition method to suppress illumination artifacts for super-resolution.

Let K be the complex line bundle where the Kostant-Souriau geometric quantization operators are deened. We discuss possible prolongations of these operators to the linear superspace of the K-valued diierential forms, such that the Poisson bracket is represented by the supercommutator of the corresponding operators. We also discuss the possibility to obtain such super-geometric quantizations by ...

For a general three dimensional theory of (super-)gravity coupled to arbitrary matter fields with arbitrary set of higher derivative terms in the effective action, we give an algorithm for consistently truncating the theory to a theory of pure (super-)gravity with the gravitational sector containing only Einstein-Hilbert, cosmological constant and Chern-Simons terms. We also outline the procedu...