Uncertainty Principle in Terms of Entropy for the Riemann-liouville Operator

نویسندگان

  • BESMA AMRI
  • LAKHDAR T. RACHDI
چکیده

We prove Hausdorff-Young inequality for the Fourier transform connected with Riemann-Liouville operator. We use this inequality to establish the uncertainty principle in terms of entropy. Next, we show that we can derive the Heisenberg-Pauli-Weyl inequality for the precedent Fourier transform.

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

Existence of Entropy Solutions for Nonsymmetric Fractional Systems

The present work focuses on entropy solutions for the fractional Cauchy problem of nonsymmetric systems. We impose sufficient conditions on the parameters to obtain bounded solutions of L∞. The solutions attained are unique and exclusive. Performance is established by utilizing the maximum principle for certain generalized time and space-fractional diffusion equations. The fractional differenti...

متن کامل

New operational matrix for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative

In this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of product based on the Bernstein basis. Then, we get the Bernstein operational matrix for the Jumarie’s modified Riemann-Liouville fractio...

متن کامل

Functional quantization and metric entropy for Riemann-Liouville processes

We derive a high-resolution formula for the L-quantization errors of Riemann-Liouville processes and the sharp Kolmogorov entropy asymptotics for related Sobolev balls. We describe a quantization procedure which leads to asymptotically optimal functional quantizers. Regular variation of the eigenvalues of the covariance operator plays a crucial role.

متن کامل

Inverse Stochastic Transfer Principle

In [10] a “direct” stochastic transfer principle was introduced, which represented multiple integrals with respect to fractional Brownian motion in terms of multiple integrals with respect to standard Brownian motion. The method employed in [10] involved an operator Γ (n) H , mapping a class of functions LH to L 2. However, the operator does not map LH onto L 2. Hence Γ (n) H is not invertible....

متن کامل

Säıd Abbas and Mouffak Benchohra UNIQUENESS RESULTS FOR FREDHOLM TYPE FRACTIONAL ORDER RIEMANN-LIOUVILLE INTEGRAL EQUATIONS

In this paper we study the existence and uniqueness of solutions of a certain Fredholm type Riemann-Liouville integral equation of two variables by using Banach contraction principle.

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 2013