共查询到20条相似文献,搜索用时 15 毫秒
1.
Zbigniew Błocki 《Expositiones Mathematicae》2009,27(2):125-135
We sketch a proof of the Ohsawa–Takegoshi extension theorem (due to Berndtsson) and then present some applications of this result: optimal lower bound for the Bergman kernel, relation to the Suita conjecture, and the Demailly approximation. 相似文献
2.
O. Lazarev and E.H. Lieb proved that, given f1,…,fn∈L1([0,1];C), there exists a smooth function Φ that takes values on the unit circle and annihilates span{f1,…,fn}. We give an alternative proof of that fact that also shows the W1,1 norm of Φ can be bounded by 5πn+1. Answering a question raised by Lazarev and Lieb, we show that if p>1 then there is no bound for the W1,p norm of any such multiplier in terms of the norms of f1,…,fn. 相似文献
3.
We give a complementary generalization of the extensions of Bonnet–Myers theorem obtained by Calabi and also Cheeger–Gromov–Taylor.
相似文献4.
《Expositiones Mathematicae》2021,39(4):515-539
The Morse–Sard theorem gives conditions under which the set of critical values of a function between Euclidean spaces has Lebesgue measure zero. Over the years the result has been extended and strengthened in various ways. We present a result, along with a simple proof, that subsumes many of these generalizations. We also review methods of constructing examples showing that differentiability hypotheses cannot be weakened, and we construct a complete set of examples for our result. 相似文献
5.
LetK
p(u1, ..., up) be the completep-partite graph whoseith vertex class hasu
i vertices (lip). We show that the theorem of Erds and Stone can be extended as follows. There is an absolute constant >0 such that, for allr1, 0<1 and=">1>1/r, every graphG=G
n of sufficiently large order |G|=n with at least
相似文献
6.
We use an inequality due to Bochnak and Lojasiewicz, which follows from the Curve Selection Lemma of real algebraic geometry
in order to prove that, given a C
r
function , we have
7.
8.
Let ? be the genealogical tree of a supercritical multitype Galton–Watson process, and let Λ be the limit set of ?, i.e., the set of all infinite self-avoiding paths (called ends) through ? that begin at a vertex of the first generation. The limit set Λ is endowed with the metric d(ζ, ξ) = 2
−n
where n = n(ζ, ξ) is the index of the first generation where ζ and ξ differ. To each end ζ is associated the infinite sequence Φ(ζ) of
types of the vertices of ζ. Let Ω be the space of all such sequences. For any ergodic, shift-invariant probability measure
μ on Ω, define Ωμ to be the set of all μ-generic sequences, i.e., the set of all sequences ω such that each finite sequence v occurs in ω with limiting frequency μ(Ω(v)), where Ω(v) is the set of all ω′?Ω that begin with the word v. Then the Hausdorff dimension of Λ∩Φ−1 (Ωμ) in the metric d is
9.
Mathematische Zeitschrift - We prove an Ohsawa–Takegoshi-type extension theorem on the Berkovich closed unit disc over certain non-Archimedean fields. As an application, we establish a... 相似文献
10.
HAI Jinke Department of Mathematics Qingdao University Qingdao China College of mathematics Shandong University Jinan China 《中国科学A辑(英文版)》2006,(5)
Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp' characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks. 相似文献
11.
Bo Berndtsson 《中国科学A辑(英文版)》2005,48(Z1)
We construct a semiexplicit integral representation of the canonical solution to the (?)-equation with respect to a plurisubharmonic weight function in a pseudoconvex domain. The construction is based on a construction related to the Ohsawa-Takegoshi extension theorem combined with a method to construct weighted integral representations due to M. Andersson. 相似文献
12.
Arnold Janssen 《Mathematische Semesterberichte》2001,48(1):103-106
In this note a direct elementary proof of Carathéodory's measure extension theorem is presented. It is based on an approximation
argument for outer measures where elements of the -algebra are approached by elements of the underlying algebra of sets with respect to the symmetric difference.
Received: 3 April 2000 / Accepted: 20 September 2000 相似文献
13.
The Ramanujan Journal - Let $$s_{q}$$ denote the sum of digits function in base q. The aim of this work is to estimate the exponential sums involving the sum of digits of shifted integers, namely... 相似文献
14.
François Laudenbach 《Comptes Rendus Mathematique》2013,351(11-12):483-488
In this Note, we give a proof of the famous theorem of M. Morse dealing with the cancellation of a pair of non-degenerate critical points of a smooth function. Our proof consists of a reduction to the one-dimensional case where the question becomes easy to answer. 相似文献
15.
B. V. Dekster 《Israel Journal of Mathematics》1985,50(3):169-180
Theorem. Let a set X?Rn have unit circumradius and let B be the unit ball containing X. Put C =conv \(\bar X\) D =diam C (=diam X), k =dim C,d i = √(2i + 2)/i. Then: (i) D∈[dn, 2]; (ii) k≧m where m∈{2,3,...,n} satisfies D∈[dm, dm?1) (di decreases by i); (iii) In case k=m (by (ii), this is always the case when m=n), C contains a k-simplex Δ such that: (α) its vertices are on δB; (β) the centre of B belongs toint Δ; (γ) the inequalitiesλ k (D) ≦l ≦D with $$\lambda _k (D) = D\sqrt {\frac{{4k - 2D^2 (k - 1)}}{{2 - (k - 2)(D^2 - 2)}}, D \in (d_k ,d_{k - 1} )} $$ are unimprovable estimates for length l of any edge of Δ. 相似文献
16.
17.
The Morse–Sard theorem states that the set of critical values of a Ck smooth function defined on a Euclidean space Rd has Lebesgue measure zero, provided k≥d. This result is hereby extended for (generalized) critical values of continuous selections over a compactly indexed countable family of Ck functions: it is shown that these functions are Lipschitz continuous and the set of their Clarke critical values is null. 相似文献
18.
This is a largely expository account of various aspects of the Borsuk–Ulam theorem, including extensions of the classical theorem to families of maps parametrized by a base space and to multivalued maps. The main technical tool is the Euler class with compact supports. 相似文献
19.
Pingping Zhang 《Linear and Multilinear Algebra》2013,61(12):2511-2517
We prove an inequality for concave functions and partitioned matrices whose numerical ranges lie in a sector. This complements a theorem by E.Y. Lee concerning the positive semi-definite case. 相似文献
20.
Archiv der Mathematik - In this note we prove a semialgebraic counterpart of Whitney’s extension theorem. 相似文献
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