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Statements

Subject Item
dbr:Jan_Mikusiński
dbo:wikiPageWikiLink
dbr:Convolution_quotient
Subject Item
dbr:Convolution_quotient
rdfs:label
Convolution quotient
rdfs:comment
In mathematics, a convolution quotient is to the operation of convolution as a quotient of integers is to multiplication. Convolution quotients were introduced by Mikusiński, and their theory is sometimes called Mikusiński's operational calculus. The kind of convolution with which this theory is concerned is defined by Convolution quotients are used in an approach to making Dirac's delta function and other generalized functions logically rigorous.
dcterms:subject
dbc:Generalized_functions
dbo:wikiPageID
51363226
dbo:wikiPageRevisionID
893540621
dbo:wikiPageWikiLink
dbr:Dirac_delta_function dbc:Generalized_functions dbr:Function_(mathematics) dbr:Generalized_function dbr:Quotient dbr:Operation_(mathematics) dbr:Convolution dbr:Titchmarsh_convolution_theorem dbr:Integer dbr:Mathematics dbr:Multiplication dbr:Rigour dbr:Operational_calculus
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n11:2r4GA wikidata:Q30704535 yago-res:Convolution_quotient
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dbo:abstract
In mathematics, a convolution quotient is to the operation of convolution as a quotient of integers is to multiplication. Convolution quotients were introduced by Mikusiński, and their theory is sometimes called Mikusiński's operational calculus. The kind of convolution with which this theory is concerned is defined by It follows from the Titchmarsh convolution theorem that if the convolution of two functions that are continuous on is equal to 0 everywhere on that interval, then at least one of is 0 everywhere on that interval. A consequence is that if are continuous on then only if This fact makes it possible to define convolution quotients by saying that for two functions ƒ, g, the pair (ƒ, g) has the same convolution quotient as the pair (h * ƒ,h * g). Convolution quotients are used in an approach to making Dirac's delta function and other generalized functions logically rigorous.
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wikipedia-en:Convolution_quotient?oldid=893540621&ns=0
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2051
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wikipedia-en:Convolution_quotient
Subject Item
dbr:Negative_probability
dbo:wikiPageWikiLink
dbr:Convolution_quotient
Subject Item
wikipedia-en:Convolution_quotient
foaf:primaryTopic
dbr:Convolution_quotient