Functional equations for peculiar functions
type: Item
instance of: scholarly article
title: Functional equations for peculiar functions
zbMATH Open document ID: 0876.39004
DOI: 10.1007/BF02215973
author: Hans-Heinrich Kairies
published in: Aequationes Mathematicae
publication date: 1997-07-20T00:00:00Z
full work available at URL: https://eudml.org/doc/137685
review text: This is a thorough and interesting survey of functional equations which characterize certain everywhere continuous nowhere differentiable functions, strictly monotonic functions with almost everywhere 0 derivatives, replicative functions (cf. \textit{D. E. Knuth} [The art of computer programming, Vol. I. (1968; Zbl 0191.17903)], etc. It concludes with some open problems and with 122 references.
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 26A27
Mathematics Subject Classification ID: 39B62
Mathematics Subject Classification ID: 26A30
zbMATH DE Number: 1019195
zbMATH Keywords: Continuous nowhere differentiable functions
zbMATH Keywords: strictly monotonic functions with almost everywhere 0 derivatives
zbMATH Keywords: Replicative functions
zbMATH Keywords: Characterizations by functional equations in a single variable
zbMATH Keywords: Peculiar functions
zbMATH Keywords: Survey
MaRDI profile type: Publication
cites work: Q4101884
cites work: Q4097001
cites work: Q4477379
cites work: Some Remarks on the Construction of Continuous Non-Differentiable Functions
cites work: Sneaky plasticity and mesoscopic fractals
cites work: Addition Theorems and Binary Expansions
cites work: Q3765729
cites work: On Van Der Waerden's Nowhere Differentiable Function
cites work: Q3329876
cites work: Q3816264
cites work: Q4483123
cites work: Q4755205
cites work: Sur une fonction réelle de Minkowski
cites work: Q5523238
cites work: Q3732220
cites work: Q5343895
cites work: Q4014263
cites work: Q3995301
cites work: Über trigonometrische Approximation und Fouriersche Reihen
cites work: The Differentiability of the Riemann Function at Certain Rational Multiples of &#960
cites work: More on the Differentiability of the Riemann Function
cites work: Q4847775
cites work: Functional equations and nowhere differentiable functions
cites work: Nowhere differentiable solutions of a system of functional equations
cites work: Constructing singular functions via Farey fractions
cites work: The Structure of Monotone Functions
cites work: Singularities of the Weierstrass type functions
cites work: Q3788227
cites work: The Takagi function and its generalization
cites work: Pointwise analysis of Riemann's ``nondifferentiable'' function
cites work: Differentiability of Riemann's function
cites work: Charakterisierung des Cotangens mit Replikativität
cites work: Zur axiomatischen Charakterisierung der Gammafunktion.
cites work: Definitionen der Bernoulli-Polynome mit Hilfe ihrer Multiplikationstheoreme
cites work: Ein Existenz- und Eindeutigkeitssatz für die Lösungen einer Funktionalgleichung aus der Nörlundschen Theorie der Differenzengleichungen
cites work: Q3889389
cites work: Q3868258
cites work: Charakterisierungen von nirgends differenzierbaren Weierstraß- Funktionen durch Replikativität. (Characterization of nowhere differentiable Weierstraß functions by replicativity)
cites work: The gamma function as continuous solution of a system of Gauss functional equations
cites work: On a characterization theorem of E. Artin
cites work: On the optimality of a characterization theorem for the gamma function using the multiplication formula
cites work: Functional equations and characterizations of Riemann's function
cites work: Q5341893
cites work: Continuous Nowhere-Differentiable Functions--an Application of Contraction Mappings
cites work: Q5518533
cites work: Ein maßtheoretischer Satz mit Anwendungen auf Funktionalgleichungen
cites work: Q5585021
cites work: On generalized Takagi functions
cites work: Q5592596
cites work: Q4040882
cites work: Zur Charakterisierung der Gamma-Funktion.
cites work: Trigonometrische Reihen Über Multiplikativen Zahlenmengen. II
cites work: The differentiability of Fourier gap series and ``Riemann's example'' of a continuous, nondifferentiable function
cites work: De Rham systems and the solution of a class of functional equations
cites work: Note on a chaotic map that generates nowhere-differentiability
cites work: Q3232379
cites work: Q3249850
cites work: Wo ist die Riemann-Funktion \(\sum_{n=1}^\infty \sin n^ 2 x / n^ 2\) nicht differenzierbar?

Functional equations for peculiar functions (cites work)
cites work: Integral Formulae of Arithmetical Character

Functional equations for peculiar functions (cites work)
cites work: Riemann's example of a continuous, 'nondifferentiable' function

Functional equations for peculiar functions (cites work)
cites work: One-parameter system of functional equations

Functional equations for peculiar functions (cites work)
cites work: Q5828139

Functional equations for peculiar functions (cites work)
cites work: Q5625500

Functional equations for peculiar functions (cites work)
cites work: Sur un exemple de fonction continue sans dérivée

Functional equations for peculiar functions (cites work)
cites work: On Singular Monotonic Functions of the Cantor Type

Functional equations for peculiar functions (cites work)
cites work: On Some Singular Monotonic Functions Which Are Strictly Increasing

Functional equations for peculiar functions (cites work)
cites work: Q4698064

Functional equations for peculiar functions (cites work)
cites work: On (\(1,b_p\))-replicative functions with isolated discontinuities

Functional equations for peculiar functions (cites work)
cites work: Q3889500

Functional equations for peculiar functions (cites work)
cites work: Riemann's example of a continuous ''nondifferentiable'' function continued

Functional equations for peculiar functions (cites work)
cites work: Integrable dynamical systems with hierarchy. II. Solutions

Functional equations for peculiar functions (cites work)
cites work: The Differentiability of Riemann's Function

Functional equations for peculiar functions (cites work)
cites work: An Increasing Continuous Singular Function

Functional equations for peculiar functions (cites work)
cites work: Eine überall stetige und nirgends differenzierbare Funktion

Functional equations for peculiar functions (cites work)
cites work: Q5831622

Functional equations for peculiar functions (cites work)
cites work: Continuous replicative functions

Functional equations for peculiar functions (Recommended article)
Recommended article: Q4722880
Similarity Score: 0.9444142
Recommender Run: Recommender Run 3

Functional equations for peculiar functions (Recommended article)
Recommended article: Q3274380
Similarity Score: 0.933956
Recommender Run: Recommender Run 3

Functional equations for peculiar functions (Recommended article)
Recommended article: Q5719093
Similarity Score: 0.93395597
Recommender Run: Recommender Run 3

Functional equations for peculiar functions (Recommended article)
Recommended article: Q5842170
Similarity Score: 0.93260026
Recommender Run: Recommender Run 3

Functional equations for peculiar functions (Recommended article)
Recommended article: Q5556825
Similarity Score: 0.93260026
Recommender Run: Recommender Run 3

Functional equations for peculiar functions (Recommended article)
Recommended article: Q5842171
Similarity Score: 0.93260026
Recommender Run: Recommender Run 3

Functional equations for peculiar functions (Recommended article)
Recommended article: Q5539083
Similarity Score: 0.9318476
Recommender Run: Recommender Run 3

Functional equations for peculiar functions (Recommended article)
Recommended article: Q3803585
Similarity Score: 0.9318476
Recommender Run: Recommender Run 3

Functional equations for peculiar functions (Recommended article)
Recommended article: On functional equations
Similarity Score: 0.9290993
Recommender Run: Recommender Run 3

Functional equations for peculiar functions (Recommended article)
Recommended article: On Some Functional Equations
Similarity Score: 0.92659634
Recommender Run: Recommender Run 3