scholarly journals Partial differential operators of infinite order with constant coefficients on the space of analytic functions on the polydisc

1990 ◽  
Vol 96 (1) ◽  
pp. 51-71 ◽  
Author(s):  
Siegfried Momm
Keyword(s):  
Analytic Functions ◽  
Infinite Order ◽  
Differential Operators ◽  
Space Of Analytic Functions ◽  
Partial Differential ◽  
Partial Differential Operators ◽  
Constant Coefficients

Real roots of polynomials and right inverses for partial differential operators in the space of tempered distributions

1990 ◽  
Vol 114 (3-4) ◽  
pp. 169-179 ◽  
Author(s):  
Michael Langenbruch
Keyword(s):  
Differential Operators ◽  
Partial Differential Operator ◽  
Continuous Linear ◽  
Real Polynomial ◽  
Partial Differential ◽  
Tempered Distributions ◽  
Real Roots ◽  
Partial Differential Operators ◽  
Constant Coefficients ◽  
Roots Of Polynomials

SynopsisLet P(D) be a partial differential operator with constant coefficients. If P(D) has a continuous linear right inverse in the space of tempered distributions, then P is the product of a polynomial without real roots and a real polynomial admitting a right inverse. If the polynomial P is real and irreducible, then P(D) admits a right inverse in the tempered distributions if and only if P(×) has the property of zeros of R. Thorn.

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