Some remarks on aplications of algebraic analysis to economics

• Authors: Zbigniew Binderman , Marek Wierzbicki
• Languages of publication: EN

Abstracts

EN

In this paper, the author continues the investigations started in his earlier work [Binderman 2009]. Here, problems of linear equation Dx=y with the difference operator D are studied. The work is an introduction to applications of the theory of right invertible operators to economics. As an example, quotations of KGHM on Warsaw Stock Exchange are considered.

Keywords

EN

algebraic analysis; right invertible operator; difference operator; quotations of Stock Exchange; Jacobian matrix

• Publisher: Katedra Ekonometrii i Statystyki, Szkoła Główna Gospodarstwa Wiejskiego w Warszawie
• Journal: Metody Ilościowe w Badaniach Ekonomicznych
• Year: 2011
• Volume: 12
• Issue: 1
• Pages: 15-26

Dates

published

2011

Contributors

author

Zbigniew Binderman

• Department of Econometrics and Statistics, Warsaw University of Live Sciences – SGGW

author

Marek Wierzbicki

• Department of Econometrics and Statistics, Warsaw University of Live Sciences – SGGW

References

• Agarwal R. P. (20000) Difference Equations and Inequalities: Theory, Methods and Applications, Marcel Dekker, New York.
• Binderman Z. (1992) Functional shifts induced by right invertible operators, Math. Nachr. 157, 211-224.
• Binderman Z. (1993) An unified approach to shifts induced by right invertible operators, Math. Nachr. 161, 239-252.
• Binderman Z. (1994) On some functional shifts induced by operators complex differentiation, Opuscula Mathematica, Vol. 14, 53-64.
• Binderman Z. (2000)On right inverses for functional shifts, Demonstratio Mathematica, Vol. XXXIII, No 3, 665-678.
• Binderman Z. (2009) On elasticity operators and their economical applications, Polish Journal an Environment Study, Vol. 18, no. 5B, 2009, s. 29-34.
• Bittner R. (1974) Rachunek operatorów w przestrzeniach liniowych, PWN Warszawa.
• Dimovski I., H. (1990) Convolutional Calculus, Kluwer Acad. Publishers, Dordrecht.
• Dimovski I., H., Hristov V., Z. (2005) Commutans of the Pommiez operator, IJMMS, Hindawi Publishing Corporation, 1239-1251.
• Douglas R.G., Shapiro H.S., Shields A.L. (1970) Cyclic vectors and invariant spaces for backward shift operator, Ann. 1’Inst. Fourier 20, 1, 37-76.
• Fage M.K., Nagnibida N.I. (1987) An equivalence problem of ordinary linear differential operators, Nauka, Novosybirsk (in Russian)
• Gelfond A.O. (1957) Calculus of finite difference, FizMatGiz, Moskva (Russian)
• Levy H., Lessman F. (1959) Finite difference equations, Pitman LTD London.
• Linchuk N. (1988) Representation of commutants of the Pommiez operator and their applications. Mat. Zamietki 44, 794-802 (in Russian)
• Przeworska-Rolewicz D. (1988) Algebraic Analysis, D. Reidel and PWN –Polish Scientific Publishers, Dordrecht-Warszawa.
• Przeworska-Rolewicz D. (1998) Logarithms and antilogarithms. An Algebraic Analysis Approach. With Appendix by Z. Binderman, Kluwer Academic Publishers, Dordrecht.
• Przeworska-Rolewicz D. (2000), Two centuries of the term “Algebraic Analysis”, Algebraic Analysis and related topics, Banach Center Publications, V.53, 47-70, Warsaw.
• Ralston A. (1965) A First Course in Numerical Analysis, McGraw-Hill Book Company.
• Sikorski R. (1969) Advanced Calculus, Function of several variables, Monografie Matematyczne, PWN Warszawa.