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Displaying similar documents to “On a functional-differential equation related to Golomb's self-described sequence”

The converse problem for a generalized Dhombres functional equation

L. Reich, Jaroslav Smítal, M. Štefánková (2005)

Mathematica Bohemica

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We consider the functional equation f ( x f ( x ) ) = ϕ ( f ( x ) ) where ϕ J J is a given homeomorphism of an open interval J ( 0 , ) and f ( 0 , ) J is an unknown continuous function. A characterization of the class 𝒮 ( J , ϕ ) of continuous solutions f is given in a series of papers by Kahlig and Smítal 1998–2002, and in a recent paper by Reich et al. 2004, in the case when ϕ is increasing. In the present paper we solve the converse problem, for which continuous maps f ( 0 , ) J , where J is an interval, there is an increasing homeomorphism ϕ of J such...

On finitely generated closed ideals in H ( D )

Jean Bourgain (1985)

Annales de l'institut Fourier

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Assume f 1 , ... , f N a finite set of functions in H ( D ) , the space of bounded analytic functions on the open unit disc. We give a sufficient condition on a function f in H ( D ) to belong to the norm-closure of the ideal I ( f 1 , ... , f N ) generated by f 1 , ... , f N , namely the property | f ( z ) | α ( | f 1 ( z ) | + ... + | f N ( z ) | ) for z D for some function α : R + R + satisfying lim t 0 α ( t ) / t = 0 . The main feature in the proof is an improvement in the contour-construction appearing in L. Carleson’s solution of the corona-problem. It is also shown that the property | f ( z ) | C max 1 j N | f j ( z ) | for z D ...

Maximal functions and capacities

Lennart Carleson (1965)

Annales de l'institut Fourier

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Pour les fonctions f ( x ) dont les coefficients de Fourier c n satisfont à Σ | c n | 2 λ n < , la capacité est évaluée pour l’ensemble où la fonction maximale satisfait à f * ( x ) λ .

Integrating factor

Jan Mařík (1994)

Mathematica Bohemica

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The problem of integrating factor for ordinary differential equations is investigated. Conditions are given which guarantee that each solution of 1 F ( x , y ) + y ' 2 F ( x , y ) = 0 is also a solution of M ( x , y ) + y ' N ( x , y ) = 0 where 1 F = μ M and 2 F = μ N .