All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 30

Showing per page

The product of a function and a Boehmian

Dennis Nemzer (1993)

Colloquium Mathematicae

Let A be the class of all real-analytic functions and β the class of all Boehmians. We show that there is no continuous operation on β which is ordinary multiplication when restricted to A.

The product of distributions on R m

Cheng Lin-Zhi, Brian Fisher (1992)

Commentationes Mathematicae Universitatis Carolinae

The fixed infinitely differentiable function ρ ( x ) is such that { n ρ ( n x ) } is a regular sequence converging to the Dirac delta function δ . The function δ 𝐧 ( 𝐱 ) , with 𝐱 = ( x 1 , ⋯ , x m ) is defined by δ 𝐧 ( 𝐱 ) = n 1 ρ ( n 1 x 1 ) ⋯ n m ρ ( n m x m ) . The product f ∘ g of two distributions f and g in 𝒟 m ' is the distribution h defined by error n 1 → ∞ ⋯ error n m → ∞ 〈 f 𝐧 g 𝐧 , φ 〉 = 〈 h , φ 〉 , provided this neutrix limit exists for all φ ( 𝐱 ) = φ 1 ( x 1 ) ⋯ φ m ( x m ) , where f 𝐧 = f * δ 𝐧 and g 𝐧 = g * δ 𝐧 .

Currently displaying 1 – 20 of 30

Page 1 Next