We extend results on constructing semiorthogonal linear spline prewavelet systems in one and two dimensions to the case of irregular dyadic refinement. In the one-dimensional case, we obtain sharp two-sided inequalities for the -condition, 1 < p < ∞, of such systems.
It is known that for determining sets Markov’s property is equivalent to Bernstein’s property. We are interested in finding a generalization of this fact for sets which are not determining. In this paper we give examples of sets which are not determining, but have the Bernstein and generalized Markov properties.
The paper is devoted to a careful analysis of the shape-preserving properties of the strongly continuous semigroup generated by a particular second-order differential operator, with particular emphasis on the preservation of higher order convexity and Lipschitz classes. In addition, the asymptotic behaviour of the semigroup is investigated as well. The operator considered is of interest, since it is a unidimensional Black-Scholes operator so that our results provide qualitative information on the...
Using some results proved in De Pascale and Pratelli [Calc. Var. Partial Differ. Equ. 14 (2002) 249-274] (and De Pascale et al. [Bull. London Math. Soc. 36 (2004) 383-395]) and a suitable interpolation technique, we show that the transport density relative to an source is also an function for any .
Using some results proved in De Pascale and Pratelli [Calc. Var. Partial Differ. Equ.14 (2002) 249-274] (and De Pascale et al. [Bull. London Math. Soc.36 (2004) 383-395]) and a suitable interpolation technique, we show that the transport density relative to an Lp source is also an Lp function for any .
The properties of shift invariant operators are proved: It is shown that Q has polynomial order r iff r is the rate of convergence of . A weak saturation theorem is given. If f is replaced by in the weak saturation formula the asymptotics of the expression is calculated. Moreover, bootstrap approximation is introduced.
The paper is concerned with the best constants in the Bernstein and Markov inequalities on a compact set . We give some basic properties of these constants and we prove that two extremal-like functions defined in terms of the Bernstein constants are plurisubharmonic and very close to the Siciak extremal function . Moreover, we show that one of these extremal-like functions is equal to if E is a nonpluripolar set with where , the supremum is taken over all polynomials P of N variables of total...
In this paper we give a characterization of -order continuity of modular function spaces in terms of the existence of best approximants by elements of order closed sublattices of . We consider separately the case of Musielak–Orlicz spaces generated by non--finite measures. Such spaces are not modular function spaces and the proofs require somewhat different methods.