Equivalent Norms for Polynomials on the Sphere

نویسندگان

  • JORDI MARZO
  • JOAQUIM ORTEGA-CERDÀ
چکیده

We find necessary and sufficient conditions for a sequence of sets EL ⊂ S in order to obtain the inequality Sd |QL|dμ ≤ Cp EL |QL|dμ, ∀L ≥ 0, where 1 ≤ p < +∞, QL is any polynomial of degree smaller or equal than L, μ is a doubling measure and the constant Cp is independent of L. From this description it follows an uncertainty principle for functions in L(S). We consider also weighted uniform versions of this result.

برای دانلود 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

A Note on the Sharpness of the Remez-type Inequality for Homogeneous Polynomials on the Sphere

A NOTE ON THE SHARPNESS OF THE REMEZ-TYPE INEQUALITY FOR HOMOGENEOUS POLYNOMIALS ON THE SPHERE M. YATTSELEV Dedicated to Ed Saff on the occasion of his 60th birthday Abstract. Remez-type inequalities provide upper bounds for the uniform norms of polynomials on given compact sets provided that for every where is a subset of of small measure. In this note we obtain an asymptotically sharp Remez-t...

متن کامل

An equivalent representation for weighted supremum norm on the upper half-plane

In this paper, rstly, we obtain some inequalities which estimates complex polynomials on the circles.Then, we use these estimates and a Moebius transformation to obtain the dual of this estimates forthe lines in upper half-plane. Finally, for an increasing weight on the upper half-plane withcertain properties and holomorphic functions f on the upper half-plane we obtain an equivalentrepresenta...

متن کامل

Spectral estimates on the sphere

In this article we establish optimal estimates for the first eigenvalue of Schrödinger operators on the d-dimensional unit sphere. These estimates depend on Lp norms of the potential, or of its inverse, and are equivalent to interpolation inequalities on the sphere. We also characterize a semi-classical asymptotic regime and discuss how our estimates on the sphere differ from those on the Eucli...

متن کامل

Gazeau- Klouder Coherent states on a sphere

In this paper, we construct the Gazeau-Klauder coherent states of a two- dimensional harmonic oscillator on a sphere based on two equivalent approaches. First, we consider the oscillator on the sphere as a deformed (non-degenerate) one-dimensional oscillator. Second, the oscillator on the sphere is considered as the usual (degenerate) two--dimensional oscillator. Then, by investigating the quan...

متن کامل

Asymptotic $L^4$ norm of polynomials derived from characters

Littlewood investigated polynomials with coefficients in {−1, 1} (Littlewood polynomials), to see how small their ratio of norms ||f ||4/||f ||2 on the unit circle can become as deg(f) → ∞. A small limit is equivalent to slow growth in the mean square autocorrelation of the associated binary sequences of coefficients of the polynomials. The autocorrelation problem for arrays and higher dimensio...

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

برای دانلود 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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007