On an Exact Estimate for a Local Theorem

1959 ◽  
Vol 4 (2) ◽  
pp. 215-218 ◽  
Author(s):  
S. Kh. Sirazhdinov
Keyword(s):  
Exact Estimate ◽  
Local Theorem

scholarly journals Exponential Codimension Growth of PI Algebras: An Exact Estimate

1999 ◽  
Vol 142 (2) ◽  
pp. 221-243 ◽  
Author(s):  
A Giambruno ◽  
M Zaicev
Keyword(s):  
Exact Estimate

An exact estimate of the second derivative in Lp

1991 ◽  
Vol 49 (5) ◽  
pp. 443-445
Author(s):  
N. Ainulloev
Keyword(s):  
Exact Estimate ◽  
Second Derivative

scholarly journals Multidimensional local theorem in the Knopfmachers semigroup

2007 ◽  
Vol 47 ◽  
Author(s):  
Rimantas Skrabutėnas
Keyword(s):  
Arithmetic Functions ◽  
Local Theorem

In the presentpaper a multidimensionallocal theorem for arithmetic functions definedin the Knopfmachers semigroup G is obtained.

The local theorem for tilings

1998 ◽  
pp. 193-199 ◽  
Author(s):  
Nikolai Dolbilin ◽  
Doris Schattschneider
Keyword(s):  
Local Theorem

scholarly journals Rank Element of a Projective Module

1965 ◽  
Vol 25 ◽  
pp. 113-120 ◽  
Author(s):  
Akira Hattori
Keyword(s):  
Finite Group ◽  
Commutative Ring ◽  
Local Ring ◽  
Projective Module ◽  
Projective Modules ◽  
Local Theorem ◽  
Complete Local Ring ◽  
A Finite Group

In § 1 of this note we first define the trace of an endomorphism of a projective module P over a non-commutative ring A. Then we call the trace of the identity the rank element r(P) of P, which we shall illustrate by several examples. For a projective module P over the groupalgebra of a finite group G, the rank element of P is essentially the character of G in P. In § 2 we prove that under certain assumption two projective modules Pi and P2 over an algebra over a complete local ring o are isomorphic if and only if their rank elements are identical. This is a type of proposition asserting that two representations are equivalent if and only if their characters are identical, and in fact, when A is the groupalgebra, the above theorem may be considered as another formulation of Swan’s local theorem [9]).

scholarly journals Integral operators, bispectrality and growth of Fourier algebras

2020 ◽  
Vol 2020 (766) ◽  
pp. 151-194 ◽  
Author(s):  
W. Riley Casper ◽  
Milen T. Yakimov
Keyword(s):  
Differential Operator ◽  
Integral Kernel ◽  
Exact Estimate ◽  
Airy Functions ◽  
Direct Computation ◽  
Infinite Dimensional ◽  
First Order ◽  
Rank 2 ◽  
Commuting Differential Operator ◽  
Algorithmic Procedure

AbstractIn the mid 1980s it was conjectured that every bispectral meromorphic function {\psi(x,y)} gives rise to an integral operator {K_{\psi}(x,y)} which possesses a commuting differential operator. This has been verified by a direct computation for several families of functions {\psi(x,y)} where the commuting differential operator is of order {\leq 6}. We prove a general version of this conjecture for all self-adjoint bispectral functions of rank 1 and all self-adjoint bispectral Darboux transformations of the rank 2 Bessel and Airy functions. The method is based on a theorem giving an exact estimate of the second- and first-order terms of the growth of the Fourier algebra of each such bispectral function. From it we obtain a sharp upper bound on the order of the commuting differential operator for the integral kernel {K_{\psi}(x,y)} leading to a fast algorithmic procedure for constructing the differential operator; unlike the previous examples its order is arbitrarily high. We prove that the above classes of bispectral functions are parametrized by infinite-dimensional Grassmannians which are the Lagrangian loci of the Wilson adelic Grassmannian and its analogs in rank 2.

scholarly journals Centrally symmetric convex bodies and sections having maximal quermassintegrals

2012 ◽  
Vol 49 (2) ◽  
pp. 189-199
Author(s):  
E. Makai ◽  
H. Martini
Keyword(s):  
Convex Body ◽  
Convex Bodies ◽  
The Body ◽  
Symmetric Convex ◽  
Local Theorem ◽  
Centrally Symmetric ◽  
Euclidean Unit Ball ◽  
Analogous Theorem ◽  
Lower Dimensional ◽  
Dimensional Surface

Let d ≧ 2, and let K ⊂ ℝd be a convex body containing the origin 0 in its interior. In a previous paper we have proved the following. The body K is 0-symmetric if and only if the following holds. For each ω ∈ Sd−1, we have that the (d − 1)-volume of the intersection of K and an arbitrary hyperplane, with normal ω, attains its maximum if the hyperplane contains 0. An analogous theorem, for 1-dimensional sections and 1-volumes, has been proved long ago by Hammer (see [2]). In this paper we deal with the ((d − 2)-dimensional) surface area, or with lower dimensional quermassintegrals of these intersections, and prove an analogous, but local theorem, for small C2-perturbations, or C3-perturbations of the Euclidean unit ball, respectively.

Local theorems and group extensions

1973 ◽  
Vol 73 (1) ◽  
pp. 7-20 ◽  
Author(s):  
Kenneth K. Hickin ◽  
Richard E. Phillips
Keyword(s):  
Local System ◽  
Local Theorem ◽  
Group Extensions ◽  
Finite Set

The concept of a local system of a set W is defined in ((8), p. 166) and ((12), p. 126). Recall that a set ℒ of subsets of W is a local system if Uℒ = W and ℒ is directed in the following sense: for every finite set H1, …, Hn of elements of ℒ, there is an M∈ℒ such that Hi⊂M for 1≤i≤n. If Σ is a class of groups, L(Σ) is the class of all groups G that possess a local system of Σ subgroups. Σ satisfies the local theorem, or is L-closed, if L(Σ)⊂Σ. Many classes of groups which satisfy the local theorem are discussed in ((12), pp. 126–144).

Sign in / Sign up

Export Citation Format

Share Document