Article

Representation of quasianalytic ultradistributions

Arkiv för matematik (impact factor: 0.45). 02/1993; 31(1):51-60. DOI:10.1007/BF02559497 pp.51-60

ABSTRACT We give the following representation theorem for a class containing quasianalytic ultradistributions and all the non-quasianalytic
ultradistributions: Every ultradistribution in this class can be written as

u = P(D)g(x) + h(x)u = P(\Delta )g(x) + h(x)

whereg(x) is a bounded continuous function,h(x) is a bounded real analytic function andP(d/dt) is an ultradifferential operator. Also, we show that the boundary value of every heat function with some exponential growth
condition determines an ultradistribution in this class. These results generalize the theorem of Matsuzawa [M] for the above
class of quasianalytic ultradistributions and partially solve a question of A. Kaneko [Ka]. Our interest lies in the quasianalytic
case, although the theorems do not exclude non-quasianalytic classes.

0 0
 · 
0 Bookmarks
 · 
17 Views
Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.

Keywords

A. Kaneko [Ka]
 
boundary value
 
bounded real analytic function andP(d/dt)
 
following representation theorem
 
heat function
 
non-quasianalytic classes
 
quasianalytic ultradistributions
 
theorem
 
theorems
 

Soon-Yeong Chung