Infinite Dimensional Bicomplex Spectral Decomposition Theorem

@article{Charak2012InfiniteDB,
  title={Infinite Dimensional Bicomplex Spectral Decomposition Theorem},
  author={Kuldeep Singh Charak and Ravinder Kumar and Dominic Rochon},
  journal={Advances in Applied Clifford Algebras},
  year={2012},
  volume={23},
  pages={593-605}
}
This paper presents a bicomplex version of the Spectral Decomposition Theorem on infinite dimensional bicomplex Hilbert spaces. In the process, the ideas of bounded linear operators, orthogonal complements and compact operators on bicomplex Hilbert spaces are introduced and treated in relation with the classical Hilbert space M′ imbedded in any bicomplex Hilbert space M. 
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References

SHOWING 1-10 OF 27 REFERENCES
Finite-Dimensional Bicomplex Hilbert Spaces
This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases,
Infinite-dimensional bicomplex Hilbert spaces
This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept
Bicomplex Riesz-Fischer Theorem
This paper continues the study of infinite dimensional bicomplex Hilbert spaces introduced in previous articles on the topic. Besides obtaining a Best Approximation Theorem, the main purpose of this
Functional Analysis: Entering Hilbert Space
This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable
Hilbert Space of the Bicomplex Quantum Harmonic Oscillator
Bicomplex numbers are pairs of complex numbers with a multiplication law that makes them a commutative ring. The problem of the quantum harmonic oscillator is investigated in the framework of
The bicomplex quantum Coulomb potential problem
Generalizations of the complex number system underlying the mathematical formulation of quantum mechanics have been known for some time, but the use of the commutative ring of bicomplex numbers for
Introduction to Hilbert spaces with applications
Normed Vector Spaces The Lebesgue Integral Hilbert Spaces and Orthonormal Systems Linear Operators on Hilbert Spaces Applications: Applications to Integral and Differential Equations Generalized
Complexified clifford analysis
The foundations of a function theory, in several complex variables, over complex Clifford algebras are developed The influence within this theory of complex analysis, in one variable, is
ON A GENERALIZED FATOU–JULIA THEOREM IN MULTICOMPLEX SPACES
In this article we introduce the hypercomplex 3D fractals generated from Multicomplex Dynamics. We generalize the well known Mandelbrot and filled-in Julia sets for the multicomplex numbers (i.e.
Multicomplex hyperfunctions
In this article, we extend our previous work on hyperfunction theory built on the space of analytic functions of one or several bicomplex variables to the multicomplex setting 𝔹ℂ n .
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