Bicomplex Riesz-Fischer Theorem

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Bicomplex Riesz-Fischer Theorem

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Abstract

This paper continues the study of infinite dimensional bicomplex Hilbert spaces introduced in previous articles on the topic. Besides obtaining a Best Approximation Theorem, themain purpose of this paper is to obtain a bicomplex analogue of the Riesz-Fischer Theorem. There are many statements of the Riesz-Fischer (R-F) Theorem in the literature, some are equivalent, some are consequences of the original versions. The one referred to in this paper is the R-F Theorem which establishes that the spaces is the canonical model space.

References

23 Cites in Article
  1. 1. V Hansen (2006). Functional Analysis: Entering Hilbert Space. Functional Analysis: Entering Hilbert Space
  2. 2. F Brackx,R Delanghe,F Sommen (1982). Clifford analysis. Clifford analysis
  3. 3. Hugo Campos,Vladislav Kravchenko (2012). Fundamentals of Bicomplex Pseudoanalytic Function Theory: Cauchy Integral Formulas, Negative Formal Powers and Schrödinger Equations with Complex Coefficients. Complex Analysis and Operator Theory, 7(2), 485-518.
  4. 4. Hugo Campos,Vladislav Kravchenko,Luis Méndez (2012). Complete Families of Solutions for the Dirac Equation Using Bicomplex Function Theory and Transmutations. Advances in Applied Clifford Algebras, 22(3), 577-594.
  5. 5. W Baylis,J Keselica (2012). The Complex Algebra of Physical Space: A Framework for Relativity. Advances in Applied Clifford Algebras, 22(3), 537-561.
  6. 6. R Delanghe,F Sommen,V Soucek (1992). Clifford analysis and spinor valued functions. Clifford analysis and spinor valued functions
  7. 7. K Charak,R Kumar,D Rochon Infinite Dimensional Bicomplex Spectral Decomposition Theorem. Adv. Appl. Clifford Algebr
  8. 8. R Lavoie,D Rochon (2012). The Bicomplex Heisenberg Uncertainty Principle, Theoretical Concepts of Quantum Mechanics. The Bicomplex Heisenberg Uncertainty Principle, Theoretical Concepts of Quantum Mechanics
  9. 9. V Hansen (2006). Functional Analysis: Entering Hilbert Space. Functional Analysis: Entering Hilbert Space
  10. 10. J Horvath (2004). On the Riesz-Fischer theorem. Studia Scientiarum Mathematicarum Hungarica, 41(4), 467-478.
  11. 11. J Neumann (1955). Review of John von Neumann,Mathematical Foundations of Quantum Mechanics, translated from the German edition by Robert T. Beyer, Princeton: Princeton University Press, 1955(1958). Physics and Philosophy, 294-298.
  12. 12. G Price (1991). An Introduction to Multicomplex Spaces and Functions. An Introduction to Multicomplex Spaces and Functions
  13. 13. V Garant–pelletier,D Rochon (2009). ON A GENERALIZED FATOU–JULIA THEOREM IN MULTICOMPLEX SPACES. Fractals, 17(03), 241-255.
  14. 14. D Rochon,M Shapiro (2004). On algebraic properties of bicomplex and hyperbolic numbers. Analele Universitatii Oradea, Fasc. Matematica, 11, 71-110.
  15. 15. J Ryan (1982). Complexified Clifford Analysis. Complex Var. Elliptic Equ, 1, 119-149.
  16. 16. G Sobczyk (1995). The hyperbolic number plane. Coll. Maths. Jour, 26, 268-280.
  17. 17. A Vajiac,M Vajiac (2012). Multicomplex hyperfunctions. Complex Variables and Elliptic Equations, 57(7-8), 751-762.
  18. 18. Raphaël Gervais Lavoie,‎louis Marchildon,Dominic Rochon (2010). Infinite-dimensional bicomplex Hilbert spaces. Annals of Functional Analysis, 1(2), 75-91.
  19. 19. R Gervais Lavoie,L Marchildon,D Rochon (2010). The Bicomplex Quantum Harmonic Oscillator. Nuovo Cimento Soc. Ital. Fis. B, 125, 1173-1192.
  20. 20. R Gervais Lavoie,L Marchildon,D Rochon (2011). Hilbert Space of the Bicomplex Quantum Harmonic Oscillator. Hilbert Space of the Bicomplex Quantum Harmonic Oscillator, 1327, 148-157.
  21. 21. J Mathieu,L Marchildon,D Rochon (2012). The bicomplex quantum Coulomb potential problem. Canadian Journal of Physics, 91(12), 1093-1100.
  22. 22. D Notes,S Rochon,Tremblay (2004). Bicomplex quantum mechanics: I. The generalized Schrödinger equation. Adv. Appl. Clifford Algebr, 14, 231-248.
  23. 23. D Rochon,S Tremblay (2006). Bicomplex Quantum Mechanics: II. The Hilbert Space. Advances in Applied Clifford Algebras, 16(2), 135-157.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

D. Rochon, Dr. K. S. Charak, Dr. R. Kumar. 1970. "Bicomplex Riesz-Fischer Theorem". Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 13 (GJSFR Volume 13 Issue F1).

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords
Classification
Primary 16D10; Secondary 30G35
46C05
46C50
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v1.2

Language
English
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Bicomplex Riesz-Fischer Theorem

D. Rochon
D. Rochon Universit du Qubec A Trois-RiviAres
Dr. Charak
Dr. Charak <p>Universit du Qubec A Trois-RiviAres</p>
R. Kumar
R. Kumar <p>Universit du Qubec A Trois-RiviAres</p>