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The Differentiable Functions from R into R n

Keiko Narita, Artur Korniłowicz, Yasunari Shidama (2012)

Formalized Mathematics

In control engineering, differentiable partial functions from R into Rn play a very important role. In this article, we formalized basic properties of such functions.

The distance between subdifferentials in the terms of functions

Libor Veselý (1993)

Commentationes Mathematicae Universitatis Carolinae

For convex continuous functions f , g defined respectively in neighborhoods of points x , y in a normed linear space, a formula for the distance between f ( x ) and g ( y ) in terms of f , g (i.eẇithout using the dual) is proved. Some corollaries, like a new characterization of the subdifferential of a continuous convex function at a point, are given. This, together with a theorem from [4], implies a sufficient condition for a family of continuous convex functions on a barrelled normed linear space to be locally uniformly...

The dual of the space of functions of bounded variation

Khaing Khaing Aye, Peng Yee Lee (2006)

Mathematica Bohemica

In the paper, we show that the space of functions of bounded variation and the space of regulated functions are, in some sense, the dual space of each other, involving the Henstock-Kurzweil-Stieltjes integral.

The factorization of f ( x ) x n + g ( x ) with f ( x ) monic and of degree 2 .

Joshua Harrington, Andrew Vincent, Daniel White (2013)

Journal de Théorie des Nombres de Bordeaux

In this paper we investigate the factorization of the polynomials f ( x ) x n + g ( x ) [ x ] in the special case where f ( x ) is a monic quadratic polynomial with negative discriminant. We also mention similar results in the case that f ( x ) is monic and linear.

The Fourier transform in Lebesgue spaces

Erik Talvila (2025)

Czechoslovak Mathematical Journal

For each f L p ( ) ( 1 p < ) it is shown that the Fourier transform is the distributional derivative of a Hölder continuous function. For each p , a norm is defined so that the space of Fourier transforms is isometrically isomorphic to L p ( ) . There is an exchange theorem and inversion in norm.

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