The completeness problem in the function algebra of linear integer-coefficient polynomials

2010 ◽  
Vol 20 (5-6) ◽  
Author(s):  
A. I. Mamontov ◽  
D. G. Meshchaninov
Keyword(s):  
Function Algebra ◽  
Integer Coefficient ◽  
Completeness Problem

Heat equation with singular potential and singular data

2005 ◽  
Vol 135 (4) ◽  
pp. 863-886 ◽  
Author(s):  
M. Nedeljkov ◽  
S. Pilipović ◽  
D. Rajter-Ćirić
Keyword(s):  
Polynomial Growth ◽  
Singular Potential ◽  
Function Algebra ◽  
Energy Estimates ◽  
Generalized Function ◽  
Type Condition ◽  
Classical Energy ◽  
The Cauchy Problem ◽  
White Noise Calculus ◽  
Singular Data

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.

Human reasoning includes a mental logic

2009 ◽  
Vol 32 (1) ◽  
pp. 96-97 ◽  
Author(s):  
David P. O'Brien
Keyword(s):  
Probability Theory ◽  
Human Reasoning ◽  
Completeness Problem ◽  
Mental Logic

AbstractOaksford & Chater (O&C) have rejected logic in favor of probability theory for reasons that are irrelevant to mental-logic theory, because mental-logic theory differs from standard logic in significant ways. Similar to O&C, mental-logic theory rejects the use of the material conditional and deals with the completeness problem by limiting the scope of its procedures to local sets of propositions.

Boundaries for a Real Function Algebra

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

Gleason Parts of a Real Function Algebra

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

scholarly journals Dual Algebras and A-Measures

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Marek Kosiek ◽  
Krzysztof Rudol
Keyword(s):  
Analytic Functions ◽  
Complete Solution ◽  
Holomorphic Functions ◽  
Classical Case ◽  
Function Algebra ◽  
Domain Of Holomorphy ◽  
Strict Pseudoconvexity ◽  
Weak Star ◽  
Spectrum Of A Function ◽  
Bounded Holomorphic

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.

The Maximal Ideal Space of Subalgebras of the Disk Algebra

1975 ◽  
Vol 18 (1) ◽  
pp. 61-65 ◽  
Author(s):  
Bruce Lund
Keyword(s):  
Unit Disk ◽  
Maximal Ideal ◽  
Function Algebra ◽  
Continuous Functions ◽  
Maximal Ideal Space ◽  
Open Unit ◽  
Ideal Space ◽  
Disk Algebra ◽  
Closed Subalgebra ◽  
Uniformly Closed

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)}.

Ring Derivations on Function Algebras

1990 ◽  
Vol 33 (1) ◽  
pp. 69-72 ◽  
Author(s):  
N. R. Nandakumar
Keyword(s):  
Function Algebra ◽  
Choquet Boundary ◽  
Function Algebras ◽  
Ring Derivation

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.

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