Spectral properties of some operator matricesSpringer Science and Business Media LLC - Tập 80 - Trang 37-46 - 2003
Il Bong Jung, Eungil Ko, Carl Pearcy
We study the classes of Jordan and n-normal operators, especially from the
standpoint of spectral properties. We show that these classes have many of the
good spectral properties of normal operators by showing this for a class of
operators that contains both of the above-mentioned classes. We then obtain
various consequences of our spectral results.
On the convergence properties of basic series representing special monogenic functionsSpringer Science and Business Media LLC - Tập 81 - Trang 62-71 - 2003
M. A. Abul-Ez, D. Constales
In this paper, it is shown that certain classes of special monogenic functions
cannot be represented by the basic series in the whole space. New definitions
for the order of basis of special monogenic polynomials are given together with
theorems on representation of classes of special monogenic functions in certain
balls and at a point.
A Trudinger–Moser inequality for a conical metric in the unit ballSpringer Science and Business Media LLC - Tập 112 - Trang 531-545 - 2019
Yunyan Yang, Xiaobao Zhu
In this note, we prove a Trudinger–Moser inequality for a conical metric in the
unit ball. Precisely, let $${\mathbb {B}}$$ be the unit ball in $${\mathbb
{R}}^N$$ $$(N\ge 2)$$ , $$p>1$$ , $$g=|x|^{\frac{2p}{N}\beta }(dx_1^2+\cdots
+dx_N^2)$$ be a conical metric on $${\mathbb {B}}$$ , and $$\lambda _p({\mathbb
{B}})=\inf \left\{ \intop _{\mathbb {B}}|\nabla u|^Ndx: u\in W_0^{1,N}({\mathbb
{B}}),\i... hiện toàn bộ