Interpolating bases for spaces of differentiable functions
Introduction to the volume
Invariance identity in the class of generalized quasiarithmetic means
An invariance formula in the class of generalized p-variable quasiarithmetic means is provided. An effective form of the limit of the sequence of iterates of mean-type mappings of this type is given. An application to determining functions which are invariant with respect to generalized quasiarithmetic mean-type mappings is presented.
Invariance of the Cauchy mean-value expression with an application to the problem of representation of Cauchy means.
Invariant graphs of functions for the mean-type mappings
Let I be a real interval, J a subinterval of I, p ≥ 2 an integer number, and M1, ... , Mp : Ip → I the continuous means. We consider the problem of invariance of the graphs of functions ϕ : Jp−1 → I with respect to the mean-type mapping M = (M1, ... , Mp).Applying a result on the existence and uniqueness of an M -invariant mean [7], we prove that if the graph of a continuous function ϕ : Jp−1 → I ...
Invariant scrambled sets and maximal distributional chaos
For the full shift (Σ₂,σ) on two symbols, we construct an invariant distributionally ϵ-scrambled set for all 0 < ϵ < diam Σ₂ in which each point is transitive, but not weakly almost periodic.
Investigation of smooth functions and analytic sets using fractal dimensions
We start from the following problem: given a function what can be said about the set of points in the range where level sets are «big» according to an opportune definition. This yields the necessity of an analysis of the structure of level sets of functions. We investigate the analogous problem for functions. These are in a certain way intermediate between and functions. The results involve a mixture of Real Analysis, Geometric Measure Theory and Classical Descriptive Set Theory.
Is the maximal function of a Lipschitz function continuous?
Iterated quasi-arithmetic mean-type mappings
We work with a fixed N-tuple of quasi-arithmetic means generated by an N-tuple of continuous monotone functions (I an interval) satisfying certain regularity conditions. It is known [initially Gauss, later Gustin, Borwein, Toader, Lehmer, Schoenberg, Foster, Philips et al.] that the iterations of the mapping tend pointwise to a mapping having values on the diagonal of . Each of [all equal] coordinates of the limit is a new mean, called the Gaussian product of the means taken on b. We effectively...
Iterates of piecewise monotonic continuous functions
Iteration groups generated by functions
Iteration semigroups with generalized convex, concave and affine elements.
Jacobi and Hankel Multipliers of Type (p,q},1<p<q<oo.
Jensen inequalities for functions with higher monotonicities.
Jensen's inequality for conditional expectations.
K základům theorie reálných čísel
Karamata's Iteration Theorem And Normed Regularly Varying Sequences In A Historical Light
Kempisty's theorem for the integral product quasicontinuity
A function f: ℝⁿ → ℝ satisfies the condition (resp. , ) at a point x if for each real r > 0 and for each set U ∋ x open in the Euclidean topology of ℝⁿ (resp. strong density topology, ordinary density topology) there is an open set I such that I ∩ U ≠ ∅ and . Kempisty’s theorem concerning the product quasicontinuity is investigated for the above notions.
Kolmogorov problem in and extremal Zolotarev ω-splines [Book]
Kontinuierliche Linearkombinationen von Strecken.