We prove that the classical Prandtl, Ishlinskii and Preisach hysteresis operators are continuous in Sobolev spaces for , (localy) Lipschitz continuous in and discontinuous in for arbitrary . Examples show that this result is optimal.
We study the continuity of pseudo-differential operators on Bessel potential spaces Hs|p (Rn ), and on the corresponding Besov spaces B^(s,q)p (R ^n). The modulus of continuity ω we use is assumed to satisfy j≥0, ∑ [ω(2−j )Ω(2j )]2 < ∞ where Ω is a suitable positive function.
We show that the restriction operator of the space of holomorphic functions on a complex Lie group to an analytic subset V has a continuous linear right inverse if it is surjective and if V is a finite branched cover over a connected closed subgroup Γ of G. Moreover, we show that if Γ and G are complex Lie groups and V ⊂ Γ × G is an analytic set such that the canonical projection is finite and proper, then has a right inverse
We study properties of the space ℳ of Borel vector measures on a compact metric space X, taking values in a Banach space E. The space ℳ is equipped with the Fortet-Mourier norm and the semivariation norm ||·||(X). The integral introduced by K. Baron and A. Lasota plays the most important role in the paper. Investigating its properties one can prove that in most cases the space is contained in but not equal to the space (ℳ,||·||(X))*. We obtain a representation of the continuous functionals on...
We determine the convolution operators on the real analytic functions in one variable which admit a continuous linear right inverse. The characterization is given by means of a slowly decreasing condition of Ehrenpreis type and a restriction of hyperbolic type on the location of zeros of the Fourier transform μ̂(z).
We study the following nonlinear method of approximation by trigonometric polynomials. For a periodic function f we take as an approximant a trigonometric polynomial of the form , where is a set of cardinality m containing the indices of the m largest (in absolute value) Fourier coefficients f̂(k) of the function f. Note that Gₘ(f) gives the best m-term approximant in the L₂-norm, and therefore, for each f ∈ L₂, ||f-Gₘ(f)||₂ → 0 as m → ∞. It is known from previous results that in the case of...