Discrete variational Green's function. I

Aequationes mathematicae -     

Green's operators

Summary Generailzed Green's functions are kernels of integral operators with certain properties. Solution operators with these properties are calledGreen's operators. Necessary and sufficient conditions for the existence of Green's operators are given for the general case, and for operators on Banach spaces. This work has been supported by Sandia Corporation, a prime contractor to the U. S. Atomic Energy Commission.     

Onp-adic Green's functions

Some classes of pseudodifferential operators over the field ofp-adic numbers and local fields with discrete valuation are studied. Sufficient conditions for the Green's functions to be non-negative are found.Institute of Mathematics, Ukrainian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 96, No. 1, pp. 123–139, July, 1993.     

Generalized Green's theories

A generalization is given of the relations and equivalences on a semigroup S associated with J. A. Green by introducing the concepts of Green's pairs and generalized Green's theories first on an arbitrary set X and finally on a semigroup S. Most of the results about the usual Green's relations and equivalences are proved, and it is shown that previous generalizations obtained by Wallace, Anscombre, Marki and Steinfeld, and Pastijn may be obtained as special cases of the theory developed. Dedicated to D. D. Miller in honor of his retirement at the University of Tennessee after 32 years of service.     

Classical equilibrium generalized hydrodynamic correlation Green's functions. I

Moscow Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 82, No. 3, pp. 450–465, March, 1990.     

Classical equilibrium generalized hydrodynamic correlation Green's functions. IV

Moscow Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 86, No. 3, pp. 460–473, March, 1991.     

余代数上的Green等价

本文在余代数上定义了五类等价关系,它们是Ｇｒｅｅｎ等价Ｇ,Ｄ,Ｌ,Ｒ,Ｈ．然 后给出了这些等价关系一些基本性质和结构特点．在每个Ｇｒｅｅｎ等价的等价类集上构 造了一种偏序并给出了偏序上半格和格结构的刻划．用Ｇ－,Ｌ－,Ｒ－类分别给出了子余 代数、左余理想、右余理想的结构刻划．进一步地,本文研究了张量积上的Ｇｒｅｅｎ等 价以及余代数同态的Ｇｒｅｅｎ保持性和提升性．作为应用,本文得到了两个不可约余代 数的张量积仍为不可约余代数的一个条件;证明了不可约余代数在Ｇ－保持余代数同 态下的同态像是不可约的．     

Variational problem of the theory of Green's potential. II

Necessary and sufficient conditions for the solvability of the problem of the minimum of the Green's energy on condensers are found. A number of properties of extremals are found.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1475–1480, November, 1990.     

A generalized Green's function

Summary We present a method in which the given boundary conditions are replaced by integral boundary conditions, so chosen that the Green's function can be constructed without changing the principal spectral properties of the operator.Translated from Litovskii Matematicheskii Sbornik, Vol. 13, No. 1, pp. 109–114, January–March, 1973.     

Investigation of p-adic Green's function

V. A. Steklov Mathematics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 87, No. 3, pp. 376–390, June, 1991     

Lattice polygons and Green's theorem

Associated to an -dimensional integral convex polytope is a toric variety and divisor , such that the integral points of represent . We study the free resolution of the homogeneous coordinate ring as a module over . It turns out that a simple application of Green's theorem yields good bounds for the linear syzygies of a projective toric surface. In particular, for a planar polytope , satisfies Green's condition if contains at least lattice points.