Ya. I. Grushka

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Articles: 4

Tachyon generalization for Lorentz transforms

Ya. I. Grushka

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 19 (2013), no. 2, 127-145

In the present paper we construct an expansion of the set of Lorentz transforms, which allows for the velocity of the reference frame to be greater than the speed of light. For maximum generality we investigate this tachyon expansion in the case of Minkowski space time over any real Hilbert space.

Direct theorems in the theory of approximation of Banach space vectors by exponential type entire vectors

Ya. Grushka, S. Torba

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 13 (2007), no. 3, 267-278

For an arbitrary operator $A$ on a Banach space $X$ which is the generator of a $C_0$--group with certain growth condition at infinity, direct theorems on connection between the degree of smoothness of a vector $x\in X$ with respect to the operator $A$, the rate of convergence to zero of the best approximation of $x$ by exponential type entire vectors for the operator $A$, and the $k$-module of continuity are established. The results allow to obtain Jackson-type inequalities in a number of classic spaces of periodic functions and weighted $L_p$ spaces.

Behavior of semigroups of normal operators in a neighborhood of zero

Ya. I. Grushka

Methods Funct. Anal. Topology 5 (1999), no. 3, 4-12

Direct approximation problems for semi-groups in Hilbert space

Ya. I. Grushka

Methods Funct. Anal. Topology 5 (1999), no. 2, 12-21


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