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

A sharp correction theorem

S. Kisliakov (1995)

Studia Mathematica

Similarity:

Under certain conditions on a function space X, it is proved that for every L ∞ -function f with ∥ f ∥ ∞ ≤ 1 one can find a function φ, 0 ≤ φ ≤ 1, such that φf ∈ X, m e s φ ≠ 1 ≤ ɛ ∥ f ∥ 1 and ∥ φ f ∥ X ≤ 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 ∞ -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

Similarity:

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 ℝ ¯ of generalized real numbers. It is worth mentioning that the algebra ℝ ¯ is not a field.

Higher-order differential systems and a regularization operator

Pavel Calábek (1999)

Mathematica Bohemica

Similarity:

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.