On the solvability of systems of linear equations on commutative semigroup

• Autorzy: Huyen N. T. T. , Tuan N. M.
• Języki publikacji: EN

Abstrakty

EN

This paper deals with the solvability of systems of linear operator equations in a linear space. Namely, the paper provides necessary and sufficient conditions for the operators under which certain kinds of systems of operator equations are solvable.

Słowa kluczowe

EN

right invertible operator; generalized invertible operator

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2010
• Tom: Vol. 43, nr 4
• Strony: 865--876
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Huyen N. T. T.

autor

Tuan N. M.

• Department of Mathematcs University of Education, Hanoi National University G7 Build., 144, Xuan Thuy Rd., Cau Giay dist. Hanoi, Vietnam,

Bibliografia

• [1] W. Dahmen, C. A. Micchelli, On multivariate E-splines, Adv. Math. 76 (1989), 33–93.
• [2] W. Dahmen, C. A. Micchelli, Local dimension of piecewise polynomial spaces, syzygies, and solutions of systems of partial differential equations, Math. Nachr. 148 (1990), 117–136.
• [3] R. Q. Jia, S. D. Riemenschneider, Z. Shen, Dimensions of kernels of linear operators, Amer. J. Math. 114 (1992), 157–184.
• [4] R. Q. Jia, S. D. Riemenschneider, Z. Shen, Solvability of systems of linear operator equations, Proc. Amer. Math. Soc. 120 (1994), 815–824.
• [5] N. V. Mau, P. T. B. Ngoc, N. M. Tuan, On the algebraic characterizations of right invertible operators of higher degree, Demonstratio Math. 40 (2007), 399–409.
• [6] D. Przeworska-Rolewicz, Algebraic Analysis, PWN-Polish Scientific Publishers, Warszawa, 1988.
• [7] S. D. Riemenschneider, R. Q. Jia, Z. Shen, Multivariate splines and dimensions of kernels of linear operators, Multivariate Approximation and Interpolation (W. Haussmann and K. Jetter, edition), Birkhauser Verlag, Basel, (1990), 261–274.
• [8] Z. Shen, Dimension of certain kernel spaces of linear operators, Proc. Amer. Math. Soc. 112 (1989), 381–390.