Vol 51, No 1 (2016)
- Year: 2016
- Articles: 5
- URL: https://journals.rcsi.science/1068-3623/issue/view/14051
Differential Equations
Spectral stability of higher order semi-elliptic operators
Abstract
The paper gives estimates for the variation of eigenvalues of Dirichlet problem for semielliptic operators with homogeneous boundary conditions upon variation of the boundary of the domain on which the problem is considered. Operators of arbitrary even order in each direction and open sets with Lipschitz smooth boundary are considered.
Real and Complex Analysis
On behavior of Fourier coefficients by Walsh system
Abstract
The paper proves that for any ε > 0 there exists ameasurable set E ⊂ [0, 1] with measure |E| > 1 − ε such that for each f ∈ L1[0, 1] there is a function \(\tilde f \in {L^1}\left[ {0,1} \right]\) coinciding with f on E whose Fourier-Walsh series converges to \(\tilde f\) in L1[0, 1]-norm, and the sequence \(\left\{ {\left| {{c_k}\left( {\tilde f} \right)} \right|} \right\}_{n = 0}^\infty \) is monotonically decreasing, where \(\left\{ {{c_k}\left( {\tilde f} \right)} \right\}\) is the sequence of Fourier-Walsh coefficients of \(\left\{ {\left| {{c_k}\left( {\tilde f} \right)} \right|} \right\}_{n = 0}^\infty \).
Two results on the normality criterion concerning holomorphic functions
Abstract
In this paper we generalize two known results concerning normal families of meromorphic functions. We first improve and extend a theorem of Liu and Nevo, using a completely different approach. Then we obtain a generalization of Gu’s normality criterion.
Frames and non linear approximations in Hilbert spaces
Abstract
A simple proof of the proposition, stated in ([2], p. 346), asserting that in Hilbert spaces a Riesz basis is greedy, is given. Also, greedy approximant for frames in Hilbert spaces is defined and it is shown that frames satisfy the quasi greedy and almost greedy conditions. Finally, we give the characterizations of approximation spaces As(Ψ), Aqs(Ψ) by means of weak-lp and Lorentz sequence spaces for frames.