Approximation of Lipschitz Functions Preserving Boundary Values
نویسندگان
چکیده
منابع مشابه
Analytic Functions and Boundary Values
Analytic functions in tubes T B = R+iB in C, where B 1⁄2 R, that generalize the Hardy H spaces are studied. The associated function M¤ of Komatsu, which is de ̄ned with the aid of certain sequences of positive real numbers, is involved in the generalizing bound of the L norm. Fourier-Laplace and Cauchy integral representations are obtained for these functions. These representations can be used t...
متن کاملClarke critical values of subanalytic Lipschitz continuous functions
We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any suba...
متن کاملAffine Approximation of Lipschitz Functions and Nonlinear Quotients
New concepts related to approximating a Lipschitz function between Banach spaces by a ne functions are introduced Results which clarify when such approximations are possible are proved and in some cases a complete characterization of the spaces X Y for which any Lipschitz function from X to Y can be so approx imated is obtained This is applied to the study of Lipschitz and uniform quotient mapp...
متن کاملAn Approximation of Jordan Decomposable functions for a Lipschitz Function
The well known Jordan decomposition theorem gives the useful characterization that any function of bounded variation can be written as the difference of two increasing functions. Functions which can be expressed in this way can be used to formulate an exclusion test for the recent Cellular Exclusion Algorithms for numerically computing all zero points or the global minima of functions in a give...
متن کاملBoundary Values of Continuous Analytic Functions
Let U, K, and C denote the open unit disc, the closed unit disc, and the unit circumference, respectively. Let A be the set of all complex-valued functions which are defined and continuous on K and analytic in U. The theorem proved in this paper states that if £ is a closed subset of C, of (Lebesgue) measure zero, and if <p is a continuous function defined on £, then there exists a function /£....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Optimization Theory and Applications
سال: 2019
ISSN: 0022-3239,1573-2878
DOI: 10.1007/s10957-019-01520-z