Development of the entire representation using the roots
Keywords:
Development, entire function, roots
Abstract
One of the most important features of the analytic function is the ability to build it by knowing its zeros.
In this work we display a point by point think about of how to build the entire function using the roots with detailed mathematical proof. The Detailed study of entire representation is given. The roots of this entire theta function and there action are highlighted. The number of the roots of Study function is same the dimension of the
nite space and characterize it.
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References
[1] A.M. Perelomov, `Generalized coherent states and their applications' (Springer, Berlin, 1986)
[2] A. Vourdas, J. Phys. A39, R65 (2006)
[3] A. Vourdas, R.F. Bishop, Phys. Rev. A50, 3331 (1994)
[4] V. Bargmann, Commun. Pure Appl. Math. 14, 187 (1961)
V. Bargmann, Commun. Pure Appl. Math. 20, 1 (1967)
[5] S. Schweber, J. Math. Phys. 3, 861 (1962)
S. Schweber, Ann. Phys.(NY) 41, 205 (1967)
[6] J. Kurchan, P. Leboeuf, M. Saraceno, Phys. Rev. A40, 6800 (1989)
A. Voros, Phys. Rev. A40, 6814 (1989)
[7] J.H. Hannay, J. Phys. A29, L101 (1996)
J.H. Hannay, J. Phys. A31, L755 (1998)
[8] N.L. Balazs, A. Voros, Phys. Rep. C143, 109 (1986)
[9] P. Leboeuf, A. Voros, J. Phys. A23, 1765 (1990)
P. Leboeuf, J. Phys. A24, 4575 (1991)
M.B. Cibils, Y. Cuche, P. Leboeuf, W.F. Wreszinski, Phys. Rev A46, 4560
(1992)
J.M. Tualle, A. Voros, Chaos, Solitons and Fractals, 5, 1085 (1995)
S. Nonnenmacher, A. Voros, J. Phys. A30, L677 (1997)
[10] H.J. Korsch, C. Muller, H. Wiescher, J. Phys. A30, L677 (1997)
F. Toscano, A.M.O. de Almeida, J. Phys. A32, 6321 (1999)
D. Biswas, S. Sinha, Phys. Rev. E60, 408 (1999)
[11] A. Vourdas, Rep. Prog. Phys. 67, 267 (2004)
[12] S. Zhang, A. Vourdas, J. Phys. A37, 8349 (2004)
S. Zhang, A. Vourdas, J. Phys. A38, 1197 (2005) (corrigendum)
[13] M. Tabuni, A. Vourdas and S. Zhang, 'Zer os in analytic representations of finite quantum systems on a torus'(Physica Scripta, 2010)
[14] S. Zhang. Quantum Phase Space Methods and Their Applications. PhD thesis, University of Bradford, UK, August 2005.
[15] S. Zhang and A. Vourdas. Analytic representation of nite quantum systems. J. Phys. A: Math. Gen., 37:8349, 2004.
[16] G. G. Athanasiu and E. G. Floratos. Coherent states in finite quantum mechanics. Nuclear Physics B, 425:343, 1994.
[17] J. Tolar and G. Chadzitaskos. Quantization on ZM and coherent states over ZM ZM: J. Phys. A, 30:2509, 1997.
[18] P. Leboeuf and A. Voros. Chaos-revealing multiplicative representation of quantum eigenstates. J. Phys. A, 23:1765, 1990.
[2] A. Vourdas, J. Phys. A39, R65 (2006)
[3] A. Vourdas, R.F. Bishop, Phys. Rev. A50, 3331 (1994)
[4] V. Bargmann, Commun. Pure Appl. Math. 14, 187 (1961)
V. Bargmann, Commun. Pure Appl. Math. 20, 1 (1967)
[5] S. Schweber, J. Math. Phys. 3, 861 (1962)
S. Schweber, Ann. Phys.(NY) 41, 205 (1967)
[6] J. Kurchan, P. Leboeuf, M. Saraceno, Phys. Rev. A40, 6800 (1989)
A. Voros, Phys. Rev. A40, 6814 (1989)
[7] J.H. Hannay, J. Phys. A29, L101 (1996)
J.H. Hannay, J. Phys. A31, L755 (1998)
[8] N.L. Balazs, A. Voros, Phys. Rep. C143, 109 (1986)
[9] P. Leboeuf, A. Voros, J. Phys. A23, 1765 (1990)
P. Leboeuf, J. Phys. A24, 4575 (1991)
M.B. Cibils, Y. Cuche, P. Leboeuf, W.F. Wreszinski, Phys. Rev A46, 4560
(1992)
J.M. Tualle, A. Voros, Chaos, Solitons and Fractals, 5, 1085 (1995)
S. Nonnenmacher, A. Voros, J. Phys. A30, L677 (1997)
[10] H.J. Korsch, C. Muller, H. Wiescher, J. Phys. A30, L677 (1997)
F. Toscano, A.M.O. de Almeida, J. Phys. A32, 6321 (1999)
D. Biswas, S. Sinha, Phys. Rev. E60, 408 (1999)
[11] A. Vourdas, Rep. Prog. Phys. 67, 267 (2004)
[12] S. Zhang, A. Vourdas, J. Phys. A37, 8349 (2004)
S. Zhang, A. Vourdas, J. Phys. A38, 1197 (2005) (corrigendum)
[13] M. Tabuni, A. Vourdas and S. Zhang, 'Zer os in analytic representations of finite quantum systems on a torus'(Physica Scripta, 2010)
[14] S. Zhang. Quantum Phase Space Methods and Their Applications. PhD thesis, University of Bradford, UK, August 2005.
[15] S. Zhang and A. Vourdas. Analytic representation of nite quantum systems. J. Phys. A: Math. Gen., 37:8349, 2004.
[16] G. G. Athanasiu and E. G. Floratos. Coherent states in finite quantum mechanics. Nuclear Physics B, 425:343, 1994.
[17] J. Tolar and G. Chadzitaskos. Quantization on ZM and coherent states over ZM ZM: J. Phys. A, 30:2509, 1997.
[18] P. Leboeuf and A. Voros. Chaos-revealing multiplicative representation of quantum eigenstates. J. Phys. A, 23:1765, 1990.
Published
2021-05-31
How to Cite
Tabuni, M. (2021). Development of the entire representation using the roots. Journal of Progressive Research in Mathematics, 18(2), 11-19. Retrieved from http://www.scitecresearch.com/journals/index.php/jprm/article/view/2042
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