On circle-Exponential Topological Algebras

Από το τεύχος 50 του περιοδικού Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

A topological algebra (,)Aτ is said to be ?circle ? exponential? if the circle ? exponential function 1exp(),!nncnωωω?+?Σ ? Α can be defined, satisfying also the property exp()exp()exp(),,:cccωθωθωθωθ+=?Α=o θω (where ).ωθωθωθ=++o The differential equation αωωα=+& can be solved in such an algebra, while each σ ? complete A ? convex algebra [1] is proved to be of the above type. Also we can formulate and solve the differential equation 00,,(TVTLτ V) αααα=+??& for each σ ? complete locally convex space (,)Vτ. It is not quite clear, which type of ? A ? convexity ? would be enough for having a circle ? exponential algebra

Σελ. 1

Σελ. 2

Σελ. 3

Σελ. 4

Σελ. 5

Σελ. 6

Σελ. 7

Σελ. 8

Σελ. 9