Construction of invariant scalar particle wave equations on Riemannian manifolds with external gauge fields

We consider the problem of constructing scalar particle wave equations in Riemannian spaces with external gauge fields whose symmetry group is the group of motions of the Riemannian space. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 237–249, August, 2008.     

A bijection between the adjoint and coadjoint orbits of a semidirect product

We prove that there exists a geometric bijection between the sets of adjoint and coadjoint orbits of a semidirect product, provided a similar bijection holds for particular subgroups. We also show that under certain conditions the homotopy types of any two orbits in bijection with each other are the same. We apply our theory to the examples of the affine group and the Poincaré group, and discuss the limitations and extent of this result to other groups.     

Absolute continuity of the Sobolev type functions on metric spaces

Under study is the absolute continuity of the functions satisfying the Poincaré inequality on s-regular metric spaces.     

Variational Formulas of Poincaré-Type Inequalities in Banach Spaces of Functions on the Line

Motivated from the study of logarithmic Sobolev, Nash and other functional inequalities, the variational formulas for Poincaré inequalities are extended to a large class of Banach (Orlicz) spaces of functions on the line. Explicit criteria for the inequalities to hold and explicit estimates for the optimal constants in the inequalities are presented. As a typical application, the logarithmic Sobolev constant is carefully examinated. Received December 13, 2001, Accepted March 26, 2002     

关于拟共形映照边界伸缩商的一个注记

本文给出了拟共形映照边界伸缩商与无限小边界伸缩商的一个等式h([μ])=inf_(μ1∈[μ])b([μ1]B)；并给出了一个关于T_0空间的推论．     

A new premium calculation principle based on Orlicz norms

A multiplicative equivalent of the zero utility premium calculation principle is introduced. If the utility function happens to be a normalized Young function the new premium calculation principle is related to Orlicz norms.     

A sharp lower bound for the first eigenvalue on Finsler manifolds

In this paper, we give a sharp lower bound for the first (nonzero) Neumann eigenvalue of Finsler-Laplacian in Finsler manifolds in terms of diameter, dimension, weighted Ricci curvature.     

A Girsanov Type Theorem on the Path Space Over a Compact Riemannian Manifold

Abstract

This article establishes a Girsanov type theorem on path spaces over compact Riemannian manifolds, generalizing the classical Girsanov theorem for Euclidean spaces.     

Liouville type results and a maximum principle for non-linear differential operators on the Heisenberg group

We prove Liouville type results for non-negative solutions of the differential inequality _Δφu?f(u)?(|_∇0u|)${\mathrm{\Delta }}_{\phi }u?f(u)?(|{\mathrm{\nabla }}_{0}u|)$ on the Heisenberg group under a generalized Keller–Osserman condition. The operator _Δφu${\mathrm{\Delta }}_{\phi }u$ is the φ  -Laplacian defined by _div0(|_∇0u|⁻¹φ(|_∇0u|)_∇0u)${\mathrm{div}}_0({|{\mathrm{\nabla }}_{0}u|}^{-1}\phi (|{\mathrm{\nabla }}_{0}u|){\mathrm{\nabla }}_{0}u)$ and φ, f and ? satisfy mild structural conditions. In particular, ? is allowed to vanish at the origin. A key tool that can be of independent interest is a strong maximum principle for solutions of such differential inequality.     

A premium principle based on the g-integral

A novel approach of calculating an insurance premium based on g-integrals and interval-valued integrals is introduced. The characterization theorem for the g-integral-based premium principle is proven, and the relations with some well-known premium principles are discussed. The main properties of the interval-valued premium principle based on the g-integral are presented and some illustrative examples are given.     

Heisenberg群上Folland—Stein定理的注记

该文在G．B．Folland与E．M．Stein研究的算子的基础上．拓展考虑了算子，其中λ＋μ≠0且λ≠α／2n，μ≠—α／2n），证明了：如果，使得有限（其中ψa，b，1（z，t）＝—4（λ＋μ）ab（｜z｜2＋1—it）a-1（｜z｜2＋1＋it）b-1，那么在分布的意义下将有．特别，当λ＝μ＝—1／2时，此结果即原来的Folland－Stein定理．     

A Restriction Theorem on the Reduced Product Heisenberg Group

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔΩｂｅａｒｅｇｕｌａｒｃｏｎｅｉｎＲｎ,Φ：Ｃｍ×Ｃｍ→Ｃｎ＝Ｒｎ＋ｉＲｎａｎΩ－ｐｏｓｉｔｉｖｅＨｅｒｍｉｔｉａｎｍａｐ．ＴｈｅＳｉｅｇｅｌｄｏｍａｉｎＤΩ,ΦｏｆｔｙｐｅｔｗｏｉｎＣｎ×ＣｍｉｓｄｅｆｉｎｅｄｂｙＤΩ,Φ＝｛（ｚ,ｗ）∈：Ｃｎ×Ｃｍ：Ｉｍｚ－Φ（ｗ,ｗ）∈Ω｝（１）（ｓｅｅ［６］）．Ｓｐｅｃｉａｌｌｙ,ｗｅａｓｓｕｍｅｔｈａｔｎ＝ｍ,Ω＝｛ｔ＝（ｔ１,ｔ２,…,ｔｎ）∈Ｒｎ：ｔｉ＞０,ｉ＝１,２,…,ｎ｝,Φ（ｕ,ｖ）＝ｕ·ｖ＝（ｕ１ｕ…     

A multiplier theorem for the sublaplacian on the Heisenberg group

A multiplier theorem for the sublaplacian on the Heisenberg group is proved using Littlewood-Paley-Stein theory ofg-functions.     

A note on the generalized Marcinkiewicz integral operators with rough kernels

In this paper,we study the generalized Marcinkiewicz integral operators MΩ,r on the product space Rn×Rm.Under the condition that Ω is a function in certain block spaces,which is optimal in some senses,the boundedness of such operators from Triebel-Lizorkin spaces to Lp spaces is obtained.     

A Note on Class Field Theory for Two-Dimensional Local Rings

The class field theory for the fraction field of a two-dimensional complete normal local ring with finite residue field is established by S. Saito. In this paper, we investigate the index of the norm group in the K ₂-idele class group for a finite Abelian extension of such fields and deduce that the existence theorem does not hold for almost fields in this case.     

A Coburn type theorem for Toeplitz operators on the Dirichlet space

A celebrated theorem of Coburn asserts that, on the setting of the Hardy space, if a Toeplitz operator is nonzero, then either it is one-to-one or its adjoint operator is one-to-one. In this paper, we show that an analogous result holds for Toeplitz operators acting on the Dirichlet space.     

A note on Rubin's methods of the use of two Euler systems

Here we show that Rubin’s method of the use of two Euler systems to the proofs of Iwasawa main conjectures of the rational number field and of an imaginary quadratic field is only proper to these two kinds of number fields. We mainly use the properties of adéle ring and idéle group in class field theory to get the result.     

关于Poincar级数算子的范数的一个注记

设无挠Ｆｕｃｈｓ群Ｔ及其子群Г’对应的Ｐｏｉｎｃａｒ级数算子为，对于Г的Ｔｅｉｃｈｍｌｌｅｒ空间Ｔ（Г）中的任意一点［ｆ］，有相应的算子，其中Гｆ＝ｆГｆ－１，从而的范数，为Ｔ（Г）上的函数．众所周知．本文证明了在整个没有小于１的上界