In this paper, we study a special class of interval translation mappings introduced in 2007 by H. Bruin. We prove that a typical map of infinite type is uniquely ergodic and provide an upper bound for the Hausdorff dimension of the parameter set that gives rise to the interval translation mappings of infinite type. Moreover, we prove that such interval translation mappings have sublinear combinatorial complexity.
The existence of weak solutions to the initial–boundary value problem for the mathematical model describing the motion of a nonlinearly elastically retarded Navier–Stokes–Voigt fluid is studied in this paper. In this model, the fluid viscosity is considered as a nonlinear function. In addition, the temperature is also taken into account, which leads to the emergence of an additional energy balance equation. The proof is based on the topological approximation approach to the study of hydrodynamic problems, as well as the following iterative process.
Some properties of the weak homological bidimension of Banach algebras are studied and important examples of its calculation are given. In particular, this characteristic is calculated for all semisimple biprojective Banach algebras with the approximation property, all so-called tensor algebras generated by bilinear forms, and all infinite-dimensional Hilbert algebras. In addition, the additivity formula for weak bidimension is proved and it is shown that, in the class of semisimple Banach algebras, this homological characteristic can take any natural values, as well as the values 0 and ∞ .
We consider complete seminormed spaces of functions of one real variable whose seminorm has a finite-dimensional kernel. If the seminorm is invariant under affine changes of the argument, we call such a space interesting. We prove that the maximal interesting space embedded in L_1,loc(ℝ^n) is equivalent to BMO , and the maximal interesting space embedded in 𝒟'(ℝ) is equivalent to the homogeneous Besov space Ḃ^0_∞,∞ . We also construct a minimal interesting space that contains the space of smooth functions with compact support.
We develop a shearlet expansion theory for the Lizorkin-type spaces 𝒮_0(ℝ^2) and 𝒮'_0(ℝ^2) . We prove that the shearlet series expansion with respect to a Parseval shearlet converges in the topology of these spaces and provide a topological characterization of the Lizorkin space of distributions in terms of shearlet coefficients. Finally, we apply our distributional shearlet expansion theory to analyze asymptotic properties of distributions and obtain several Tauberian-type results that characterize the quasiasymptotics and quasiasymptotically boundedness of Lizorkin distributions via the asymptotic behavior of their shearlet coefficients.
