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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Banach--Colmez spaces
巴拿赫-科尔梅斯空间 黑匣子 [LB18， §2]
2023/5/8
Explain [LB18, §2]. Then state [LB18, Thm 4.1] and prove some of the cases, using [LB18, §3] as a black box.
Banach space theory is the main theme of this proposal. This theory has a long history going back to the pioneering works by Stefan Banach in the 1930s. It is well-known nowadays that Banach space the...
GIAMBELLI AND DEGENERACY LOCUS FORMULAS FOR CLASSICAL G/P SPACES
LOCUS FORMULAS GIAMBELLI
2015/12/17
Let G be a classical complex Lie group, P any parabolic subgroup
of G, and X = G/P the corresponding homogeneous space, which parametrizes
(isotropic) partial flags of subspaces of a fix...
Trace coordinates on Fricke spaces of some simple hyperbolic surfaces
simple hyperbolic surfaces Fricke spaces
2015/9/29
The work of Fricke-Klein [20] develops the deformation theory of hyperbolic
structures on a surface Σ in terms of the space of representations of its fundamental group damental group π = π1(Σ) in SL(...
RELATIVE VIRTUAL LOCALIZATION AND VANISHING OF TAUTOLOGICAL CLASSES ON MODULI SPACES OF CURVES
VIRTUAL LOCALIZATION VANISHING
2015/7/14
We prove a localization formula for the moduli space of stable relative maps.
As an application, we prove that all codimension i tautological classes on the moduli space
of stable pointed curves van...
RELATIVE VIRTUAL LOCALIZATION AND VANISHING OF TAUTOLOGICAL CLASSES ON MODULI SPACES OF CURVES
VIRTUAL LOCALIZATION VANISHING
2015/7/14
We prove a localization formula for the moduli space of stable relative maps.
As an application, we prove that all codimension i tautological classes on the moduli space
of stable pointed curves van...
Let G be a classical complex Lie group, P any parabolic subgroup
of G, and G/P the corresponding partial flag variety. We prove an explicit
combinatorial Giambelli formula which expresses an a...
Real-Variable Theory and Fourier Integral Operators on Semisimple Lie Groups and Symmetric Spaces of Real Rank One
Real-Variable Theory Fourier Integral Operators Semisimple Lie Groups Symmetric Spaces Real Rank One
2014/4/3
Let G be a non-compact connected semisimple Lie group of real rank one with finite center, K a maximal compact subgroup of G and X = G/K an associated symmetric space of real rank one. We will p...
Angles and a Classification of Normed Spaces
generalized angle normed space Functional Analysis
2012/7/9
We suggest a concept of generalized `angles' in arbitrary real normed vector spaces. We give for each real number a definition of an `angle' by means of the shape of the unit ball. They all yield the ...
Pointwise multipliers of Calderón-Lozanovskii spaces
Banach ideal spaces Banach function spaces Calderon-Lozanovskii spaces symmetric spaces Orlicz spaces sequence spaces
2012/6/30
Several results concerning multipliers of symmetric Banach function spaces are presented firstly. Then the results on multipliers of Calder\'on-Lozanovskii spaces are proved. We investigate assumption...
Heat equation for weighted Banach space valued function spaces
Laplace operator holomorphic semigroups weighted Banach space valued function spaces Functional Analysis
2012/6/21
We study the homogeneous equation (*) $ u' = \Delta u$, $t > 0$, $u(0)=f\in wX$, where $wX$ is a weighted Banach space, $w(x)= (1+||x||)^k$, $x\in \r^n$ with $k\ge 0$, $ \Delta$ is the Laplacian, $Y$ ...
Heat kernel generated frames in the setting of Dirichlet spaces
Heat kernel Gaussian bounds Functional calculus Sampling Frames Besov spaces
2012/6/19
Wavelet bases and frames consisting of band limited functions of nearly exponential localization on Rd are a powerful tool in harmonic analysis by making various spaces of functions and distributions ...
Weighted Lipschitz estiamtes for commutators of one-sided operators on one-sided Triebel-Lizorkin spaces
one-sided weight weighted Lipschitz function one-sided Triebel-Lizorkin space one-sided singular integral
2012/6/15
Using the extrapolation of one-sided weights, we establish the boundedness of commutators generated by weighted Lipschitz functions and one-sided singular integral operators from weighted Lebesgue spa...
Hypercyclic operators on countably dimensional spaces
Cyclic operators hypercyclic operators invariant subspaces topological vector spaces
2012/5/25
According to Grivaux, the group $GL(X)$ of invertible linear operators on a separable infinite dimensional Banach space $X$ acts transitively on the set $\Sigma(X)$ of countable dense linearly indepen...
Anisotropic Function Spaces on Singular Manifolds
Anisotropic weighted Sobolev spaces Bessel potential spaces Besov spaces Holder spaces noncomplete Riemannian manifolds with boundary
2012/4/18
A rather complete investigation of anisotropic Bessel potential, Besov, and H\"older spaces on cylinders over (possibly) noncompact Riemannian manifolds with boundary is carried out. The geometry of t...