Global smoothness preservation and the variation-diminishing property.
Hausdorff measures of the set of critical values of functions of the class
Hölder continuous functions on compact sets and functions spaces
Hölder functions in Bergman type spaces
It seems impossible to extend the boundary value theory of Hardy spaces to Bergman spaces since there is no boundary value for a function in a Bergman space in general. In this article we provide a new idea to show what is the correct version of Bergman spaces by demonstrating the extension to Bergman spaces of a result of Hardy-Littlewood in Hardy spaces, which characterizes the Hölder class of boundary values for a function from Hardy spaces in the unit disc in terms of the growth of its derivative....
Holomorphic Sobolev spaces on the ball [Book]
Homogeneous Besov spaces on locally compact Vilenkin groups
Idempotents in quotients and restrictions of Banach algebras of functions
Let be the Beurling algebra with weight on the unit circle and, for a closed set , let . We prove that, for , there exists a closed set of measure zero such that the quotient algebra is not generated by its idempotents, thus contrasting a result of Zouakia. Furthermore, for the Lipschitz algebras and the algebra of absolutely continuous functions on , we characterize the closed sets for which the restriction algebras and are generated by their idempotents.
Instability of the eikonal equation and shape from shading
In the shape from shading problem of computer vision one attempts to recover the three-dimensional shape of an object or landscape from the shading on a single image. Under the assumptions that the surface is dusty, distant, and illuminated only from above, the problem reduces to that of solving the eikonal equation |Du|=f on a domain in . Despite various existence and uniqueness theorems for smooth solutions, we show that this problem is unstable, which is catastrophic for general numerical algorithms. ...
Interpolating bases for spaces of differentiable functions
Is the maximal function of a Lipschitz function continuous?
Kolmogorov problem in and extremal Zolotarev ω-splines [Book]
Lipschitz Classes and Restrictions of Fourier Transforms.
Lipschitz conditions on the modulus of a harmonic function.
Lipschitz differences and Lipschitz functions
Lipschitz extensions of convex-valued maps
Si dimostra che ogni funzione multivoca lipschitziana con costante di Lipschitz , definita su un sottoinsieme di uno spazio di Hilbert a valori compatti e convessi in , può essere estesa su tutto ad una funzione multivoca lipschitziana con costante minore di 7 nM. In generale, non esistono invece estensioni aventi la stessa costante di Lipschitz .
Lipschitz r-continuity of the approximative subdifferential of a convex function.
Mean value theorem for convex functionals
Measure theoretic zero sets in infinite dimensional spaces and differentiability of Lipschitz mappings
Metric diophantine approximation in Julia sets of expanding rational maps
Necessary conditions for the Fourier coefficients of periodic functions to belong to B(p, k, )-classes of Besov type.