Translation invariant linear operators and generalized functions
نویسندگان
چکیده
منابع مشابه
Translation-invariant linear operators
The theory of translation-invariant operators on various spaces of functions (or measures or distributions) is a well-trodden field. The problem is to decide, first, whether or not a linear operator between two function spaces on, say, IR or R + which commutes with one or many translations on the two spaces is necessarily continuous, and, second, to give a canonical form for all such continuous...
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Let us denote V, the finite dimensional vector spaces of functions of the form ψ(x) = pn(x)+ f(x)pm(x) where pn(x) and pm(x) are arbitrary polynomials of degree at most n andm in the variable x while f(x) represents a fixed function of x. Conditions onm,n and f(x) are found such that families of linear differential operators exist which preserve V. A special emphasis is accorded to the cases wh...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1975
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1975.101311