Note on Reflexive Algebras with Non—distributive Invariant Lattices

§０．　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＬｂｅａｃｏｌｌｅｃｔｉｏｎｏｆｃｌｏｓｅｄｓｕｂｓｐａｃｅｓｏｆａＨｉｌｂｅｒｔｓｐａｃｅＨｃｏｎｔａｉｎｉｎｇ｛０｝ａｎｄＨｗｈｉｃｈｆｏｒｍｓａｃｏｍｐｌｅｔｅｓｕｂｓｐａｃｅｌａｔｔｉｃｅｕｎｄｅｒｔｈｅｏｐｅｒａｔｉｏｎｓ∧（ｉｎｔｅｒｓｅｃｔｉｏｎ）ａｎｄ∨（ｃｌｏｓｅｄｌｉｎｅａｒｓｐａｎ）．ＷｅｄｅｎｏｔｅｂｙａｌｇＬｔｈｅａｌｇｅｂｒａｏｆａｌｌｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓｗｈｉｃｈｌｅａｖｅａｌｌｓｕｂｓｐａｃｅｓｉｎＬｉ…     

Travelling Wave Solutions for Generalized Fisher Equation

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ［１，２］，ＡｒｏｎｓｏｎａｎｄＷｅｉｎｂｅｒｇｅｒｈａｖｅｓｔｕｄｉｅｄｓｙｓｔｅｍａｔｉｃｌｙｔｈｅｓｃａｌａｒｎｏｎｌｉｎｅａｒｄｉｆｆｕ－ｓｉｏｎｅｑｕａｔｉｏｎｉｎｏｎｅｓｐａｃｅｖａｒｉａｂｌｅｕｔ＝ｕｘｘ＋φ（ｕ），（１．１）ｗｈｅｒｅｕ＝ｕ（ｘ，ｔ）ａｎｄφ（ｕ）ｉｓａｎｏｎｌｉｎｅａｒｆｕｎｃｔｉｏｎ．Ｅｑｕａｔｉｏｎ（１．１）ａｒｉｓｅｓｉｎｓｅｖｅｒａｌａｐｐｌｉｃａ－ｔｉｏｎｓ；Ｓｅｅ［１，２］ａｎｄ［３］ｆｏｒｉｎｆｏｒｍａｔｉｏｎａ…     

A Property of Solutions for Elliptic Equation with Nonstandard Growth Conditions in Unbounded Domain

§０．　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔΩｂｅａｎｕｎｂｏｕｎｄｅｄｄｏｍａｉｎｉｎｔｈｅｎ－ｄｉｍｅｎｓｉｏｎａｌＥｕｃｌｉｄｅａｎｓｐａｃｅＥｎ（ｎ３）．Ｃｏｎｓｉｄｅｒ－ｉｎｇｔｈｅｆｏｌｌｏｗｉｎｇｅｌｌｉｐｔｉｃｅｑｕａｔｉｏｎｗｉｔｈｎｏｎｓｔａｎｄａｒｄｇｒｏｗｔｈｃｏｎｄｉｔｉｏｎｓ：－ｄｉｖＡ（ｘ,ｕ,ｕ）＝Ｂ（ｘ,ｕ,ｕ）（１）ｗｈｅｒｅＡ（ｘ,ｕ,ξ）＝｛Ａｉ（ｘ,ｕ,ξ）,ｉ＝１,２,…,ｎ｝ａｎｄＢ（ｘ,ｕ,ξ）ａｒｅｄｅｆｉｎｅｄｏｎＥｎ×Ｅ１×Ｅｎ,ｃｏｎ－…     

On Some Properties of Infinite-dimensional Bers Fiber Space

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅＴｅｉｃｈｍüｌｅｒｓｐａｃｅｓｄｉｓｃｕｓｓｅｄｉｎｔｈｉｓｐａｐｅｒａｒｅｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎａｌＴｅｉｃｈｍüｌｅｒｓｐａｃｅｓｗｉｔｈｃｏｍｐｌｅｘｓｔｒｕｃｔｕｒｅ．Ｔｈｉｓｉｍｐｌｉｅｓｔ...     

REALHYPERSURFACESWITHCONSTANTPRINCIPALCURVATUREINCOMPLEXHYPERBOLICSPACES

ＡｂｓｔｒａｃｔＬｅｔＭｂｅａｒｅａｌｈｙｐｅｒｓｕｒｆａｃｅｗｉｔｈｔｈｒｅｅ．ｄｉｓｔｉｎｃｔｃｏｎｓｔａｎｔｐｒｉｎｃｉｐａｌｃｕｒ－ｖａｔｕｒｅｓｉｎｔｗｏｄｉｍｅｎｓｉｏｎａｌｃｏｍｐｌｅｘｈｙｐｅｒｂｏｌｉｃｓｐａｃｅＣＨ，ｔｈｅｎｅｉｔｈｅｒ（ａ）Ｍｈａｓｔｗｏｐｒｉｎｃｉｐａｌｃｕｒｖａｔｕｒｅｓｗｈｏｓｅｄｉｆｆｅｒｅｎｃｅｉｓｌａｒｇｅｔｈａｎｚｅｒｏａｎｄｌｅｓｓｔｈａｎｏｎｅ．（ｂ）ＴｈｅｔｈｒｅｅｐｒｉｎｃｉｐａｌｃｕｒｖａｔｕｒｅｓｏｆＭｆｏｒｍａｎｅｑｕｉｄｉｆｆｅｒｅｎｃｅｓｅｑｕｅｎｃｅｗｈｏｓｅｃｏｍｍｏｎｄｉｆｆｅｒｅｎｃｅｉｓｏｎｅ；（ｃ）Ｍｉｓｈｏｌｏｍｏｒｐｈｉｃｃｏｎｇｒｕｅｎｔｔｏａｎｏｐｅｎｐａｒｔｏｆａｔｕｂｅａｒｏｕｎｄｒｅａｌｔｗｏｄｉｍｅｎｔｉｏｎａｌｈｙｐｅｒｂｏｌｉｃｓｐａｃｅ．．Ｋｅｙｗｏｒｄｓ．Ｒｅａｌｈｙｐｅｒｓｕｒｆａｃｅｃｏｍｐｌｅｘｈｙｐｅｒｂｏｌｉｃｓｐａｃｅｔｕｂｅｌｅｑｕｉｄｉｆｆｅｒｅｎｃｅｓｅｑｕｅｎｃｅ     

Involution Fixing∪from (i=1) to r(RP(1))~m_i×(CP(1))~s_i*)

§０．ＩｎｔｒｏｄｕｃｔｉｏｎＷｅｗｒｉｔｅＦＰ（ｎ）ｆｏｒＣＰ（ｎ）（ｎ－ｄｉｍｅｎｓｉｏｎａｌｃｏｍｐｌｅｘｐｒｏｊｅｃｔｉｖｅｓｐａｃｅ）ｏｒＨＰ（ｎ）（ｎ－ｄｉ－ｍｅｎｓｉｏｎａｌｑｕａｔｅｒｎｉｏｎｉｃｐｒｏｊｅｃｔｉｖｅｓｐａｃｅ）．Ｍｎ...     

On the Order of Best Approximation by Polynomials in H_q~p Spaces

ＯｎｔｈｅＯｒｄｅｒｏｆＢｅｓｔＡｐｐｒｏｘｉｍａｔｉｏｎｂｙＰｏｌｙｎｏｍｉａｌｓｉｎＨ■ＳｐａｃｅｓＸｉｎｇＦｕｃｈｏｎｇ（邢富冲）（ＣｅｎｔｒａｌＵｎｉｖｅｒｓｉｔｙｆｏｒＮａｔｉｏｎａｌｉｔｉｅｓ，Ｂｅｉｊｉｎｇ，１０００８１）Ｃｏｍｍｕｎｉ...     

2—Harmonic Totally Real Submanifolds in a Complex Projective Space

２－ＨａｒｍｏｎｉｃＴｏｔａｌｌｙＲｅａｌＳｕｂｍａｎｉｆｏｌｄｓｉｎａＣｏｍｐｌｅｘ　Ｐｒｏｊｅｃｔｉｖｅ　ＳｐａｃｅＳｕｎＨｏｎｇａｎ（孙弘安）（ＳｏｕｔｈｅｒｎＩｎｓｔｉｔｕｔｅｏｆＭｅｔａｌｌｕｒｇｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ...     

The Continuity of Epimorphisms of Banach Algebras

ＬｅｔｆｂｅａｌｉｎｅａｒｍａｐｐｉｎｇｆｒｏｍａＢａｎａｃｈｓｐａｃｅＸｔｏａＢａｎａｃｈｓｐａｃｅＹ．Ｔｈｅｎｔｈｅｓｅｐａｒａｔｉｎｇｓｐａｃｅｏｆｆｉｓ（ｆ）＝｛ｙ∈Ｙ：ｔｈｅｒｅｅｘｉｓｔｓａｓｅｑｕｅｎｃｅ（ｘｎ）ｉｎＸｗｉｔｈｘｎ０ａ...     

Two Questions on Local Properties

ＬｅｔＸｂｅａｓｐａｃｅ ,ａｎｄＱａｔｏｐｏｌｏｇｉｃａｌｐｒｏｐｅｒｔｙ .Ｉｆｆｏｒｅａｃｈｘ∈Ｘ ,ｔｈｅｒｅｅｘｉｓｔｓａｎｅｉｇｈｂｏｒｈｏｏｄＵｏｆｘｓｕｃｈｔｈａｔＵｈａｓｐｒｏｐｅｒｔｙＱ ,ｔｈｅｎｗｅｃａｌｌＸａｌｏｃａｌＱ ｓｐａｃｅ .　Ｄｅｆｉｎｉｔｉｏｎ 1　ＡｓｐａｃｅＸｉｓｃａｌｌｅｄθ ｒｅｆｉｎａｂｌｅ,ｉｆｆｏｒｅｖｅｒｙｏｐｅｎｃｏｖｅｒＵｏｆＸｔｈｅｒｅｅｘｉｓｔｓａｓｅｑｕｅｎｃｅ {Ｕｎ}ｏｆｏｐｅｎｒｅｆｉｎｅｍｅｎｔｓｏｆＵｓｕｃｈｔｈａｔｆｏｒｅａｃｈｘ∈Ｘ ,…     

Averaged Wave Operators and Complex-symmetric Operators

We study the behaviour of sequences \(U_2^n X U_1^{-n}\), where \(U_1, U_2\) are unitary operators, whose spectral measures are singular with respect to the Lebesgue measure, and the commutator \(XU_1-U_2X\) is small in a sense. The conjecture about the weak averaged convergence of the difference \(U_2^n X U_1^{-n}-U_2^{-n} X U_1^n\) to the zero operator is discussed and its connection with complex-symmetric operators is established in a general situation. For a model case where \(U_1=U_2\) is the unitary operator of multiplication by z on \(L^2(\mu )\), sufficient conditions for the convergence as in the Conjecture are given in terms of kernels of integral operators.     

算子的拟相似与(Q)类算子

本文引进定义于L(H)上的集值函数β(S)和(Q)类算子(指本质谱含于其一切拟相似算子的本质谱的算子),用β(S)刻划 (Q)类算子的特征;证明(Q)类算子范围广泛,次可分解算子(包括次标量算子,M-亚正常算子,半亚正常算子等等)是其中的一部分;(Q)类算子在L(H)中稠密.     

Continuity of Operators Intertwining with Convolution Operators

Let G be a locally compact abelian group, let μ be a bounded complex-valued Borel measure on G, and let T_μ be the corresponding convolution operator on L¹(G). Let X be a Banach space and let S be a continuous linear operator on X. Then we show that every linear operator Φ: X→L¹(G) such that ΦS=T_μΦ is continuous if and only if the pair (S,T_μ) has no critical eigenvalue.     

Pseudodifferential Operators Associated with a Semigroup of Operators

Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifolds, fractals, graphs etc.). Boundedness on L ^p for pseudodifferential operators of order 0 is proved. We mainly focus on symbols belonging to the class $S^{0}_{1,\delta}$ for δ∈[0,1). For the limit class $S^{0}_{1,1}$ , we describe some results by restricting our attention to the case of a sub-Laplacian operator on a Riemannian manifold.     

Sampling of Operators

Sampling and reconstruction of functions is a fundamental tool in science. We develop an analogous sampling theory for operators whose Kohn-Nirenberg symbols are bandlimited. We prove sampling theorems for in this sense bandlimited operators and show that our results generalize both, the classical sampling theorem, and the fact that a time-invariant operator is fully determined by its impulse response.     

可亚正规化的算子

最近,Ky Fan在[1]中就有限维希尔伯特空间引进了所谓可正规化算子的概念,考察了这类算子的一系列特征,其实在[1]中给出的可正规化算子的概念推广到无限维的Hilbert空间时,所列出的绝大部分特征也是成立的,希氏空间H上的线性有界算子T称为可正规化的,是指存在H上的可逆算子S,使S~*TS是正规算子。     

Intertwining Operators Associated to a Family of Differential-Reflection Operators

Mediterranean Journal of Mathematics - We introduce a family of differential-reflection operators $${\Lambda_{A, \varepsilon}}$$ acting on smooth functions defined on $${{\mathbb R}}$$ . Here, A is...     

单调算子和强制算子的相补问题

讨论了单调算子和强制算子的相补问题，给出了解的存在性定理。并进一步证明了严格单调算子的解的唯一定理。     

S-Storage Operators

In 1990, J. L. Krivine introduced the notion of storage operator to simulate, for Church integers, the “call by value” in a context of a “call by name” strategy. In the present paper we define for every λ-term S which realizes the successor function on Church integers the notion of S-storage operator. We prove that every storage operator is an S-storage operator. But the converse is not always true.     

Spectralizable Operators

We introduce the notion of spectralizable operators. A closed operator A in a Hilbert space is called spectralizable if there exists a non-constant polynomial p such that the operator p(A) is a scalar spectral operator in the sense of Dunford. We show that such operators belongs to the class of generalized spectral operators and give some examples where spectralizable operators occur naturally. Vladimir Strauss gratefully acknowledges support by DFG, Grant No. TR 903/3-1.