منابع مشابه
Stability of Discrete Stokes Operators in Fractional Sobolev Spaces
Using a general approximation setting having the generic properties of finite-elements, we prove uniform boundedness and stability estimates on the discrete Stokes operator in Sobolev spaces with fractional exponents. As an application, we construct approximations for the timedependent Stokes equations with a source term in L(0, T ;L(Ω)) and prove uniform estimates on the time derivative and di...
متن کاملA monotonicity result for discrete fractional difference operators
In this note we demonstrate that if y(t) ≥ 0, for each t in the domain of t → y(t), and if, in addition, Δ0y(t) ≥ 0, for each t in the domain of t → Δ0y(t), with 1 < ν < 2, then it holds that y is an increasing function of t. This demonstrates that, in some sense, the positivity of the νth order fractional difference has a strong connection to the monotonicity of y. Furthermore, we provide a du...
متن کاملConditioning Analysis of Nonlocal Integral Operators in Fractional Sobolev Spaces
We study the condition number of the stiffness matrix arising from finite element discretizations of nonlocal integral operators with singular and integrable kernels. Such operators are used in nonlocal diffusion, peridynamics formulation of continuum mechanics, image processing, and phase transition. We quantify of the extremal eigenvalues with respect to all underlying parameters; the horizon...
متن کاملOn Discrete Fractional Integral Operators and Mean Values of Weyl Sums
In this paper we prove new ` → ` bounds for a discrete fractional integral operator by applying techniques motivated by the circle method of Hardy and Littlewood to the Fourier multiplier of the operator. From a different perspective, we describe explicit interactions between the Fourier multiplier and mean values of Weyl sums. These mean values express the average behaviour of the number rs,k(...
متن کاملSliding discrete fractional transforms
Fractional transforms are useful tools for processing of non-stationary signals. The methods of implementing sliding discrete fractional Fourier transform (SDFRFT), sliding discrete fractional cosine transform (SDFRCT) and sliding discrete fractional sine transform (SDFRST) for real time processing of signals are presented. The performances of these sliding transforms, with regard to computatio...
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: Applicable Analysis and Discrete Mathematics
سال: 2015
ISSN: 1452-8630,2406-100X
DOI: 10.2298/aadm150218007a