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On Linear Functional Equations with Nonpolynomial C ∞ Solutions

Published online by Cambridge University Press:  20 November 2018

Halina Światak
Halina Światak*
Affiliation:
Jagello University, Cracow, Poland, McGill University, Montreal, Quebec
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It is known (cf. M. A. McKiernan [6]) that the only measurably bounded solutions ƒ of the equations

1

where x ∊ Rn , t ∊ R, αi(i= 1, …, m) span the space , and Σi ∊ 1 μi ≠0 for any I ⊂ {1, …, m}, are polynomials. The degree of these polynomials and the dimension of the solution space can be estimated by numbers depending on m and n. (For estimates and other details concerning equations (1) see see [1], [2], [3], [4], [5], [6].)

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 239 - 244
Copyright
Copyright © Canadian Mathematical Society 1971

References

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