Acta Mathematica
1871-2509
Cơ quản chủ quản: Springer Netherlands , INT PRESS BOSTON, INC
Lĩnh vực:
Mathematics (miscellaneous)
Phân tích ảnh hưởng
Thông tin về tạp chí
Các bài báo tiêu biểu
Sur une relation donnée par M. Cayley, dans la théorie des fonctions elliptiques
Tập 1 - Trang 368-370 - 1882
K-homology and index theory on contact manifolds
Tập 213 - Trang 1-48 - 2014
This paper applies K-homology to solve the index problem for a class of hypoelliptic (but not elliptic) operators on contact manifolds. K-homology is the dual theory to K-theory. We explicitly calculate the K-cycle (i.e., the element in geometric K-homology) determined by any hypoelliptic Fredholm operator in the Heisenberg calculus. The index theorem of this paper precisely indicates how the analytic versus geometric K-homology setting provides an effective framework for extending formulas of Atiyah–Singer type to non-elliptic Fredholm operators.
Operator-Lipschitz functions in Schatten–von Neumann classes
Tập 207 - Trang 375-389 - 2012
This paper resolves a number of problems in the perturbation theory of linear operators, linked with the 45-year-old conjecure of M. G. Kreĭn. In particular, we prove that every Lipschitz function is operator-Lipschitz in the Schatten–von Neumann ideals S
α
, 1 < α < ∞. Alternatively, for every 1 < α < ∞, there is a constant c
α
> 0 such that
$$ {\left\| {f(a) - f(b)} \right\|_{\alpha }} \leqslant {c_{\alpha }}{\left\| f \right\|_{{{\text{Lip}}\,{1}}}}{\left\| {a - b} \right\|_{\alpha }}, $$
where f is a Lipschitz function with
$$ {\left\| f \right\|_{{{\text{Lip}}\,{1}}}}: = \mathop{{\sup }}\limits_{{_{{\lambda \ne \mu }}^{{\lambda, \mu \in \mathbb{R}}}}} \left| {\frac{{f\left( \lambda \right) - f\left( \mu \right)}}{{\lambda - \mu }}} \right| < \infty, $$
$$ {\left\| \cdot \right\|_{\alpha }} $$
is the norm is S
α
, and a and b are self-adjoint linear operators such that
$$ a - b \in {S^{\alpha }} $$
.