977,366 research outputs found
Weingarten integration over noncommutative homogeneous spaces
We discuss an extension of the Weingarten formula, to the case of
noncommutative homogeneous spaces, under suitable "easiness" assumptions. The
spaces that we consider are noncommutative algebraic manifolds, generalizing
the spaces of type , with
being subgroups of the unitary group, subject to certain uniformity conditions.
We discuss various axiomatization issues, then we establish the Weingarten
formula, and we derive some probabilistic consequences.Comment: 22 page
Moduli Spaces of Embedded Constant Mean Curvature Surfaces with Few Ends and Special Symmetry
We give necessary conditions on complete embedded \cmc surfaces with three or
four ends subject to reflection symmetries. The respective submoduli spaces are
two-dimensional varieties in the moduli spaces of general \cmc surfaces. We
characterize fundamental domains of our \cmc surfaces by associated great
circle polygons in the three-sphere.Comment: latex2e, AMS-latex, 24 page
Intertwining Operators And Quantum Homogeneous Spaces
In the present paper the algebras of functions on quantum homogeneous spaces
are studied. The author introduces the algebras of kernels of intertwining
integral operators and constructs quantum analogues of the Poisson and Radon
transforms for some quantum homogeneous spaces. Some applications and the
relation to -special functions are discussed.Comment: 20 pages. The general subject is quantum groups. The paper is written
in LaTe
On the Cauchy--Rassias Inequality and Linear n-Inner Product Preserving Mappings
We prove the Cauchy-Rassias stability of linear n-inner product preserving
mappings in -inner product Banach spaces. We apply the Cauchy-Rassias
inequality that plays an influencial role in the subject of functional
equations. The inequality was introduced for the first time by Th.M.Rassias in
his paper entitled: On the stability of the linear mapping in Banach spaces,
Proc. Amer. Math.Soc. 72(1978), 297-300.Comment: 13 pages, Added references, and title and abstract change
Inhomogeneous parabolic equations on unbounded metric measure spaces
We study inhomogeneous semilinear parabolic equations with source term f
independent of time u_{t}={\Delta}u+u^{p}+f(x) on a metric measure space,
subject to the conditions that f(x)\geq 0 and u(0,x)=\phi(x)\geq 0. By
establishing Harnack-type inequalities in time t and some powerful estimates,
we give sufficient conditions for non-existence, local existence, and global
existence of weak solutions. This paper generalizes previous results on
Euclidean spaces to general metric measure spaces
- …