Expand all Collapse all | Results 1 - 8 of 8 |
1. CMB Online first
On an Exponential Functional Inequality and its Distributional Version Let $G$ be a group and $\mathbb K=\mathbb C$ or $\mathbb
R$.
In this article, as a generalization of the result of Albert
and Baker,
we investigate the behavior of bounded
and unbounded functions $f\colon G\to \mathbb K$ satisfying the inequality
$
\Bigl|f
\Bigl(\sum_{k=1}^n x_k
\Bigr)-\prod_{k=1}^n f(x_k)
\Bigr|\le \phi(x_2, \dots, x_n),\quad \forall\, x_1, \dots,
x_n\in G,
$
where $\phi\colon G^{n-1}\to [0, \infty)$. Also, as a distributional
version of the above inequality we consider the stability of
the functional equation
\begin{equation*}
u\circ S - \overbrace{u\otimes \cdots \otimes u}^{n-\text {times}}=0,
\end{equation*}
where $u$ is a Schwartz distribution or Gelfand hyperfunction,
$\circ$ and $\otimes$ are the pullback and tensor product of
distributions, respectively, and $S(x_1, \dots, x_n)=x_1+ \dots
+x_n$.
Keywords:distribution, exponential functional equation, Gelfand hyperfunction, stability Categories:46F99, 39B82 |
2. CMB 2011 (vol 56 pp. 44)
Polystable Parabolic Principal $G$-Bundles and Hermitian-Einstein Connections We show that there
is a bijective correspondence between the polystable parabolic
principal $G$-bundles and solutions of the Hermitian-Einstein
equation.
Keywords:ramified principal bundle, parabolic principal bundle, Hitchin-Kobayashi correspondence, polystability Categories:32L04, 53C07 |
3. CMB 2011 (vol 54 pp. 593)
Stability of Real $C^*$-Algebras We will give a characterization of stable real $C^*$-algebras
analogous to the one given for complex $C^*$-algebras by Hjelmborg
and RÃ¸rdam. Using this result, we will prove
that any real $C^*$-algebra satisfying the corona factorization
property is stable if and only if its complexification is stable.
Real $C^*$-algebras satisfying the corona factorization property
include AF-algebras and purely infinite $C^*$-algebras. We will also
provide an example of a simple unstable $C^*$-algebra, the
complexification of which is stable.
Keywords:stability, real C*-algebras Category:46L05 |
4. CMB 2010 (vol 54 pp. 364)
Lyapunov Theorems for the Asymptotic Behavior of Evolution Families on the Half-Line
Two theorems regarding the
asymptotic behavior of evolution families are established in
terms of the solutions of a certain Lyapunov operator equation.
Keywords:evolution families, exponential instability, Lyapunov equation Categories:34D05, 47D06 |
5. CMB 2009 (vol 53 pp. 218)
Restriction of the Tangent Bundle of $G/P$ to a Hypersurface Let P be a maximal proper parabolic subgroup of a connected simple linear algebraic group G, defined over $\mathbb C$, such that $n := \dim_{\mathbb C} G/P \geq 4$. Let $\iota \colon Z \hookrightarrow G/P$ be a reduced smooth hypersurface of degree at least $(n-1)\cdot \operatorname{degree}(T(G/P))/n$. We prove that the restriction of the tangent bundle $\iota^*TG/P$ is semistable.
Keywords:tangent bundle, homogeneous space, semistability, hypersurface Categories:14F05, 14J60, 14M15 |
6. CMB 2006 (vol 49 pp. 358)
On the Principal Eigencurve of the $p$-Laplacian: Stability Phenomena We show that each point of the principal eigencurve of the
nonlinear problem
$$
-\Delta_{p}u-\lambda m(x)|u|^{p-2}u=\mu|u|^{p-2}u \quad
\text{in } \Omega,
$$
is stable (continuous) with respect to the exponent $p$ varying in
$(1,\infty)$; we also prove some convergence results
of the principal eigenfunctions corresponding.
Keywords:$p$-Laplacian with indefinite weight, principal eigencurve, principal eigenvalue, principal eigenfunction, stability Categories:35P30, 35P60, 35J70 |
7. CMB 2000 (vol 43 pp. 418)
Obstructions to $\mathcal{Z}$-Stability for Unital Simple $C^*$-Algebras Let $\cZ$ be the unital simple nuclear infinite dimensional
$C^*$-algebra which has the same Elliott invariant as $\bbC$,
introduced in \cite{JS}. A $C^*$-algebra is called $\cZ$-stable
if $A \cong A \otimes \cZ$. In this note we give some necessary
conditions for a unital simple $C^*$-algebra to be $\cZ$-stable.
Keywords:simple $C^*$-algebra, $\mathcal{Z}$-stability, weak (un)perforation in $K_0$ group, property $\Gamma$, finiteness Category:46L05 |
8. CMB 1998 (vol 41 pp. 49)
Stability of weighted darma filters We study the stability of linear filters associated with certain types of
linear difference equations with variable coefficients. We show that
stability is determined by the locations of the poles of a rational transfer
function relative to the spectrum of an associated weighted shift operator.
The known theory for filters associated with constant-coefficient difference
equations is a special case.
Keywords:Difference equations, adaptive $\DARMA$ filters, weighted shifts,, stability and boundedness, automatic continuity Categories:47A62, 47B37, 93D25, 42A85, 47N70 |