2 7 N ov 2 00 1 Derivatives of the L p - cosine transform

نویسنده

  • Yossi Lonke
چکیده

The L-cosine transform of an even, continuous function f ∈ Ce(S ) is defined by: H(x) = ∫ S |〈x, ξ〉|f(ξ) dξ, x ∈ R. It is shown that if p is not an even integer then all partial derivatives of even order of H(x) up to order p + 1 (including p + 1 if p is an odd integer) exist and are continuous everywhere in R\{0}. As a result of the corresponding differentiation formula, we show that if f is a positive bounded function and p > 1 then H is a support function of a convex body whose boundary has everywhere positive Gauss-Kronecker curvature.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

ar X iv : q ua nt - p h / 02 11 05 7 v 1 1 1 N ov 2 00 2 Recursive Weak - and Strong Coupling Expansions in a Cosine Potential

For the Cos(2x)-Potential the coefficients of the weak-and strong coupling perturbation series of the ground state energy are constructed recur-sively. They match the well-known expansion coefficients of the Mathieu equation's characteristic values. However presently there is no physically intuitive method to extract the coefficients of the strong coupling series from those of the weak one. The...

متن کامل

ar X iv : 0 70 7 . 40 06 v 1 [ he p - th ] 2 6 Ju l 2 00 7 Two - loop Gell - Mann – Low function of N = 1 supersymmetric

Two-loop Gell-Mann–Low function of N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives. Abstract Two-loop Gell-Mann–Low function is calculated for N=1 supersymmetric Yang– Mills theory, regularized by higher covariant derivatives. The integrals, which define it, are shown to be reduced to total derivatives and can be easily calculated analytically .

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2001