Tuesday 6 January 2015

Operator Algebra Note 1 Differential Operator and Symbol / February 24, 2008

Operator Algebra

Note 1
Differential Operator and Symbol 

TANAKA Akio


1
Complex variant partial differential operator     z
Multi-index     α = α1, …, αn)  0n
zα: = z1α1, …, znαn
α! = α1!...αn!
|α| = j
2
Topological space     X
All of X’s open sets     (X)
U  (X)
Regular function f(z) : U  
All of regular functions over U     (U)
Sheaf      (n U  (U)
3
(zz) = α(z)zα, aα(z)(Ucn)
P’s order     Minimum of m
4
Sequence { aα(z)}α∈N0n(Ucn)
5
{|α| ; z  K } = 0
6
Differential operator of infinite order     (zz) = α(z)zα, aα(z)(Ucn)
7
 ς= (ς1, …,ςn) n
Symbol     (zς) : = α(zα
8
All of differential operators of infinite order       Sheaf of  linear space, expressed by c

[Reference]
<On infinite order, refer to the next.>
Operator Algebra / Conjecture 1 / Order of Word / February 16, 2008


Tokyo February 24, 2008

Sekinan Research Field of Language

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