In this work, we aim to prove algebra properties for generalized Sobolev spaces W ∩L on a Riemannian manifold, whereW s,p is of Bessel-typeW s,p := (1+L)(L) with an operator L generating a heat semigroup satisfying off-diagonal decays. We don’t require any assumption on the gradient of the semigroup. To do that, we propose two different approaches (one by a new kind of paraproducts and another ...

1. Overview 2 2. Electromagnetic waves 3 2.1. Approximate cloaking via change of variables 3 2.1.1. Cloaking for the Helmholtz equation 3 2.1.2. Full range estimates for the degree of invisibility 4 2.1.3. Perfect cloaking for the Helmholtz equation 4 2.2. Electrical impedance tomography 5 2.3. Generalized impedance boundary conditions 5 2.3.1. The Helmholtz equation 6 2.3.1. The time harmonic ...

‎by considering a degenerate $p(x)-$laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent sobolev space is presented‎. ‎multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding nehari manifold‎.

In view of the good properties of nonstationary wavelet frames and the better flexibility of wavelets in Sobolev spaces, the nonstationary dual wavelet frames in a pair of dual Sobolev spaces are studied in this paper. We mainly give the oblique extension principle and the mixed extension principle for nonstationary dual wavelet frames in a pair of dual Sobolev spaces H(R) and H−s(Rd). Keywords...

In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded multiplication operator, for a large class of weights. To have bounded multiplication operator has important consequences in Approximation Theory: it implies the unif...

The present paper is devoted to analyzing the lack of compactness bounded sequences in inhomogeneous Sobolev spaces, where might fail be compact due an isometric group action, that is, translation. It will proved every sequence (un) has (possibly infinitely many) profiles, and then asymptotically decomposed into a sum translated profiles double-suffix residual term, term becomes arbitrarily sma...

In this paper, we derive error estimates for generalized interpolation, in particular collocation, in Sobolev spaces. We employ our estimates to collocation problems using radial basis functions and extend and improve previously known results for elliptic problems. Finally, we use meshless collocation to approximate Lyapunov functions for dynamical systems.

In this paper the wavelet transformation on Gelfand and Shilov spaces of type WM ( ), W (∆) and W M (∆ ) is studied. It is shown that Wψφ :WM ( )→WM ( n × +), Wψφ :W Ω (∆)→W (∆ × +) andWψφ :W M (∆)→W M (∆ × +) is linear and continuous where n and ∆ are n-dimensional real numbers and complex numbers. A boundedness result in a generalized Sobolev space is derived.