Vol 52, No 1 (2017)

In the present paper we study the Finslerian hypersurfaces of a Finsler space with a special (α, β) metric, and examine the hypersurfaces of this special metric as a hyperplane of first, second and third kinds.

In this paper we study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems by using new fixed point results of mixed monotone operators on cones.

In the framework of von Neumann’s description of measurements of discrete quantum observables we establish a one-to-one correspondence between symmetric statistical operators W of quantum mechanical systems and classical point processes κ_W, thereby giving a particle picture of indistinguishable quantum particles. This holds true under irreducibility assumptions if we fix the underlying complete orthonormal system. The method of the Campbell measure is developed for such statistical operators; it is shown that the Campbell measure of a statistical operator W coincides with the Campbell measure of the corresponding point process κ_W. Moreover, again under irreducibility assumptions, a symmetric statistical operator is completely determined by its Campbell measure. Themethod of the Campbell measure then is used to characterize Bose-Einstein and Fermi-Dirac statistical operators. This is an elementary introduction into the work of Fichtner and Freudenberg [10, 11] combined with the quantum mechanical investigations of [2] and the corresponding point process approach of [30]. It is based on the classical work of von Neumann [22], Segal, Cook and Chaiken [7, 8, 28] as well as Moyal [18].

The present paper is devoted to the Lusin’s approximation of functions from Hajłasz–Sobolev classes M_α^p(X) for p > 0. It is proved that for any f ∈ M_α^p(X) and any ε > 0 there exist an open set O_ε ⊂ X with measure less than ε (as a measure can be taken the corresponding capacity or Hausdorff content) and an approximating function f_ε such that f = f_ε on XO_ε. Moreover, the correcting function f_ε is regular (that is, it belongs to the underlying space M_α^p(X) and it is a locally Hölder function), and it approximates the original function in the metric of the space M_α^p(X).

In this paper we deal with a special double sine trigonometric series formed by its blocks. This type of trigonometric series is of particular interest since its blocks always are bounded, that is, under some additional assumptions the sum-function of such series always exists. We give some conditions under which such sum-function is integrable of power p ∈ {2, 3,... }, as well as is integrable with some natural weight.