Skip to main content
SpringerLink
Log in

On Some Problems Concerning a Sum Type Operator

  • Chapter
  • First Online:
Functional Equations in Mathematical Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 52))

  • 1577 Accesses

Abstract

Several open problems are presented that are connected with the sum type operator of the form:

$$F[\varphi ](x) := \sum\limits_{k=0}^{\infty }\ \frac{1} {{2}^{k}}\varphi ({2}^{k}x).$$

They concern the images and pre-images of the operator, its spectral properties, its maximal domain and possible extensions.

Mathematics Subject Classification (2000): Primary: 47B38; Secondary: 26A27, 39B22

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Baron, K., Kairies, H.-H.: Characterizations of eigenspaces by functional equations. Aequationes Math. 68, 248–259 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Kairies, H.-H.: Functional equations and characterizations of classes of particular function series. Prace Matem. 17, 151–164 (2000)

    MathSciNet  MATH  Google Scholar 

  3. Kairies, H.-H.: On a Banach space automorphism and its connections to functional equations and continuous nowhere differentiable functions. Ann. Acad. Paed. Cracoviensis Studia Mathematica 1, 39–48 (2001)

    Google Scholar 

  4. Kairies, H.-H.: On an operator preserving lacunarity of Fourier series. Aequationes Math. 62, 1–8 (2001)

    Article  MathSciNet  Google Scholar 

  5. Kairies, H.-H.: Properties of an operator acting on the space of bounded real functions and certain subspaces. In: (eds. Z. Daróczy, Z. Palés) Functional Equations - Results and Advances, pp. 175–186, Kluwer Acad. Publishers, Boston-Dordrecht-London (2001)

    Google Scholar 

  6. Kairies, H.-H.: Spectra of certain operators and iterative functional equations. Ann. Acad. Paed. Cracoviensis Studia Mathematica 2, 13–22 (2002)

    Google Scholar 

  7. Kairies, H.-H.: On continuous and residual spectra of operators connected with iterative functional equations. Ann. Acad. Paed. Cracoviensis Studia Mathematica 5, 52–57 (2006)

    MathSciNet  Google Scholar 

  8. Kairies, H.-H., Volkmann, P.: Ein Vektorraumisomorphismus vom Summentyp. Seminar LV 13 (2002). http://www.mathematik.uni-karlsruhe.de/~semlv

  9. Kôno, N.: On generalized Takagi functions. Acta Math. Hungar. 49, 315–324 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  10. Makó, J., Páles, Z.: Approximate convexity of Takagi type functions. J. Math. Anal. Appl. 369, 545–554 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mikolás, M.: Construction des familles de fonctions partout continues non dérivables. Acta Sci. Math. Szeged 17, 49–62 (1956)

    MathSciNet  MATH  Google Scholar 

  12. Tabor, Ja., Tabor, Jó.: Takagi functions and approximate midconvexity. J. Math. Anal. Appl. 356, 729–737 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Clausthal, Erzstraße 1, D-38678, Clausthal-Zellerfeld, Germany

    Hans-Heinrich Kairies

Authors
  1. Hans-Heinrich Kairies
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hans-Heinrich Kairies .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, National Technical University of Athens, Iroon Polytechneiou 9, Athens, 15780, Greece

    Themistocles M. Rassias

  2. Institute of Mathematics, Pedagogical University, ul. Podchorazych 2, Krakow, 30-084, Poland

    Janusz Brzdek

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Kairies, HH. (2011). On Some Problems Concerning a Sum Type Operator. In: Rassias, T., Brzdek, J. (eds) Functional Equations in Mathematical Analysis. Springer Optimization and Its Applications(), vol 52. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0055-4_34

Download citation

Publish with us

Policies and ethics

Search

Navigation