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

Previous Page 3 Next

Displaying 41 – 60 of 90

Showing per page

The modified Cauchy transformation with applications to generalized Taylor expansions

Bogdan Ziemian (1992)

Studia Mathematica

We generalize to the case of several variables the classical theorems on the holomorphic extension of the Cauchy transforms. The Cauchy transformation is considered in the setting of tempered distributions and the Cauchy kernel is modified to a rapidly decreasing function. The results are applied to the study of "continuous" Taylor expansions and to singular partial differential equations.

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 .

The space D ( U ) is not B r -complete

Manuel Valdivia (1977)

Annales de l'institut Fourier

Certain classes of locally convex space having non complete separated quotients are studied and consequently results about B r -completeness are obtained. In particular the space of L. Schwartz D ( Ω ) is not B r -complete where Ω denotes a non-empty open set of the euclidean space R m .

Currently displaying 41 – 60 of 90