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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed-norm of orthogonal projections and analytic interpolation on dimensions of measures
正交投影 混合范数 度量维度 分析插值
2023/5/5
We obtain new mixed-norm estimates and geometric results on projections. In the proof we introduce a new quantity called s-amplitude, and interpolate analytically not only on p,q, but also on dimensio...
Finding approximately rank-one submatrices with the nuclear norm and l1 norm
rank-one submatrices the nuclear norm and l1 norm
2010/11/15
We propose a convex optimization formulation with the nuclear norm and $\ell_1$-norm to find a large approximately rank-one submatrix of a given nonnegative matrix. We develop optimality conditions f...
The norm of the Euler class
norm Euler class
2010/12/6
We prove that the norm of the Euler class E for flat vector bundles is 2−n (in even dimension n, since it vanishes in odd dimension). This shows that the Sullivan–Smillie bound considered by Gro...
Amemiya Norm Equals Orlicz Norm in Generalized Orlicz Spaces
Musielak--Orlicz space Luxemburg norm Orlicz norm Amemiya norm
2007/12/10
Let $(\Omega ,\mu )$ be a $\sigma $-finite measure space and $\Phi :\Omega \times \lbrack 0,\infty )\rightarrow \lbrack 0,\infty ]$ be a Musielak--Orlicz function. Denote by $L^{\Phi }(\Omega )$ the M...
Let $p(z)$ be a monic polynomial of degree $n$, with complex coefficients, and let $q(z)$ be its monic factor. We prove an asymptotically sharp inequality of the form $\|q\|_{E} \le C^n \|p\|_E$, whe...
In this paper, we will define the inner-product and the norm in taxicab geometry and then we will discuss this inner-product geometrically.