Function algebra methods

Author(s):  
Lawrence Zalcman
Keyword(s):  

Author(s):  
M. Nedeljkov ◽  
S. Pilipović ◽  
D. Rajter-Ćirić

Nets of Schrödinger C0-semigroups (Sε)ε with the polynomial growth with respect to ε are used for solving the Cauchy problem (∂t − Δ)U + VU = f(t, U), U(0, x) = U0(x) in a suitable generalized function algebra (or space), where V and U0 are singular generalized functions while f satisfies a Lipschitz-type condition. The existence of distribution solutions is proved in appropriate cases by the means of white noise calculus as well as classical energy estimates.





2020 ◽  
pp. 136-163
Author(s):  
S. H. Kulkarni ◽  
B.V. Limaye


2020 ◽  
pp. 89-135
Author(s):  
S. H. Kulkarni ◽  
B.V. Limaye




2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Marek Kosiek ◽  
Krzysztof Rudol

Weak-star closures of Gleason parts in the spectrum of a function algebra are studied. These closures relate to the bidual algebra and turn out both closed and open subsets of a compact hyperstonean space. Moreover, weak-star closures of the corresponding bands of measures are reducing. Among the applications we have a complete solution of an abstract version of the problem, whether the set of nonnegative A-measures (called also Henkin measures) is closed with respect to the absolute continuity. When applied to the classical case of analytic functions on a domain of holomorphyΩ⊂Cn, our approach avoids the use of integral formulae for analytic functions, strict pseudoconvexity, or some other regularity ofΩ. We also investigate the relation between the algebra of bounded holomorphic functions onΩand its abstract counterpart—thew* closure of a function algebraAin the dual of the band of measures generated by one of Gleason parts of the spectrum ofA.



1975 ◽  
Vol 18 (1) ◽  
pp. 61-65 ◽  
Author(s):  
Bruce Lund

Let X be a compact Hausdorff space and C(X) the complexvalued continuous functions on X. We say A is a function algebra on X if A is a point separating, uniformly closed subalgebra of C(X) containing the constant functions. Equipped with the sup-norm ‖f‖ = sup{|f(x)|: x ∊ X} for f ∊ A, A is a Banach algebra. Let MA denote the maximal ideal space.Let D be the closed unit disk in C and let U be the open unit disk. We call A(D)={f ∊ C(D):f is analytic on U} the disk algebra. Let T be the unit circle and set C1(T) = {f ∊ C(T): f'(t) ∊ C(T)}.



1990 ◽  
Vol 33 (1) ◽  
pp. 69-72 ◽  
Author(s):  
N. R. Nandakumar

AbstractIn this paper we show that a ring derivation on a function algebra is trivial provided that the Choquet boundary of the algebra contains a dense sequentially non-isolated set.



1970 ◽  
Vol 11 (2) ◽  
pp. 233-243 ◽  
Author(s):  
E A Gorin
Keyword(s):  


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