Solvability of systems of linear operator equations

Authors:
Rong Qing Jia, Sherman Riemenschneider and Zuowei Shen

Journal:
Proc. Amer. Math. Soc. **120** (1994), 815-824

MSC:
Primary 47A50; Secondary 39A70

MathSciNet review:
1169033

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a semigroup of commuting linear operators on a linear space with the group operation of composition. The solvability of the system of equations , where and , was considered by Dahmen and Micchelli in their studies of the dimension of the kernel space of certain linear operators. The compatibility conditions , are necessary for the system to have a solution in . However, in general, they do not provide sufficient conditions. We discuss what kinds of conditions on operators will make the compatibility sufficient for such systems to be solvable in .

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1994-1169033-1

Keywords:
Systems of operator equations,
multivariate approximation,
polynomial ideals,
linear partial differential equations,
linear partial difference equations

Article copyright:
© Copyright 1994
American Mathematical Society