منابع مشابه
Twice Differentiable Spectral Functions
A function F on the space of n × n real symmetric matrices is called spectral if it depends only on the eigenvalues of its argument. Spectral functions are just symmetric functions of the eigenvalues. We show that a spectral function is twice (continuously) differentiable at a matrix if and only if the corresponding symmetric function is twice (continuously) differentiable at the vector of eige...
متن کاملOn The Leibniz Rule And Fractional Derivative For Differentiable And Non-Differentiable Functions
In the recent paper Communications in Nonlinear Science and Numerical Simulation. Vol.18. No.11. (2013) 2945-2948, it was demonstrated that a violation of the Leibniz rule is a characteristic property of derivatives of non-integer orders. It was proved that all fractional derivatives Dα, which satisfy the Leibniz rule Dα(fg) = (Dαf) g+ f (Dαg), should have the integer order α = 1, i.e. fraction...
متن کاملFinely Differentiable Monogenic Functions
Since 1970’s B. Fuglede and others have been studying finely holomorhic functions, i.e., ‘holomorphic’ functions defined on the so-called fine domains which are not necessarily open in the usual sense. This note is a survey of finely monogenic functions which were introduced in [12] like a higher dimensional analogue of finely holomorphic functions.
متن کاملInference on Directionally Differentiable Functions
This paper studies an asymptotic framework for conducting inference on parameters of the form φ(θ0), where φ is a known directionally differentiable function and θ0 is estimated by θ̂n. In these settings, the asymptotic distribution of the plug-in estimator φ(θ̂n) can be readily derived employing existing extensions to the Delta method. We show, however, that the “standard” bootstrap is only cons...
متن کاملEssentially Strictly Differentiable Lipschitz Functions
In this paper we address some of the most fundamental questions regarding the diierentiability structure of locally Lipschitz functions deened on Banach spaces. For example, we examine the relationship between inte-grability, D-representability and strict diierentiability. In addition to this, we show that on a large class of Banach spaces there is a signiicant family of locally Lipschitz funct...
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 Mathematical Analysis and Applications
سال: 2001
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7656