6533b827fe1ef96bd128714b
RESEARCH PRODUCT
Nonradial Hormander algebras of several variables and convolution operators
Siegfried MommJosé BonetAntonio Galbissubject
Pure mathematicsOperator (computer programming)Applied MathematicsGeneral MathematicsZero (complex analysis)Holomorphic functionEven and odd functionsConvolution powerQuotientMathematicsAnalytic functionConvolutiondescription
A characterization of the closed principal ideals in nonradial Hormander algebras of holomorphic functions of several variables in terms of the behaviour of the generator is obtained. This result is applied to study the range of convolution operators and ultradifferential operators on spaces of quasianalytic functions of Beurling type. Contrary to what is known to happen in the case of non-quasianalytic functions, an ultradistribution on a space of quasianalytic functions is constructed such that the range of the operator does not contain the real analytic functions. Let u, v : R → R be continuous, non-negative and even functions which are increasing on the positive real numbers. We assume that v is convex and the quotient u(x) v(x) tends to zero as x → ∞. Both functions are extended to R as follows: u(x1, . . . , xN ) := N ∑ i=1 u(xi), v(x1, . . . , xN ) := N ∑
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-02-07 |