Some problems arising from prediction theory and a theorem of Kolmogorov.

José J. Guadalupe Hernández; José L. Rubio de Francia

Displaying similar documents to “Some problems arising from prediction theory and a theorem of Kolmogorov.”

A sharp correction theorem

S. Kisliakov (1995)

Studia Mathematica

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Under certain conditions on a function space X, it is proved that for every $L^{\infty}$ -function f with $∥ f ∥_{\infty} \leq 1$ one can find a function φ, 0 ≤ φ ≤ 1, such that φf ∈ X, $m e s φ \neq 1 \leq ɛ ∥ f ∥_{1}$ and $∥ φ f ∥_{X} \leq c o n s t (1 + l o g ɛ^{- 1})$ . For X one can take, e.g., the space of functions with uniformly bounded Fourier sums, or the space of $L^{\infty}$ -functions on $ℝ^{n}$ whose convolutions with a fixed finite collection of Calderón-Zygmund kernels are also bounded.

On systems of linear algebraic equations in the Colombeau algebra

Jan Ligęza, Milan Tvrdý (1999)

Mathematica Bohemica

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From the fact that the unique solution of a homogeneous linear algebraic system is the trivial one we can obtain the existence of a solution of the nonhomogeneous system. Coefficients of the systems considered are elements of the Colombeau algebra $\bar{ℝ}$ of generalized real numbers. It is worth mentioning that the algebra $\bar{ℝ}$ is not a field.

Higher-order differential systems and a regularization operator

Pavel Calábek (1999)

Mathematica Bohemica

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Sufficient conditions for the existence of solutions to boundary value problems with a Caratheodory right hand side for ordinary differential systems are established by means of continuous approximations.

Generalisation of a Number-Theoretical Result

Štefan Znám (1966)

Matematicko-fyzikálny časopis

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A weighted Plancherel formula. III. The case of the hyperbolic matrix ball.

Jaak Peetre, Gen Kai Zhang (1992)

Collectanea Mathematica

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On exceptions to Szegedy's theorem

M. Chaimovich, G. Freimann, J. Schönheim (1987)

Acta Arithmetica

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