Skip to main content
SpringerLink
Log in

The Reproducing Kernel Property and Its Space: The Basics

  • Reference work entry
  • First Online:
Operator Theory

Abstract

This is the first part of the exposition which appears in this handbook under the common title “The Reproducing Kernel Property and Its Space.”

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 999.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
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. Aronszajn, N.: La théorie des noyaux reproduisants et ses applications. I. Proc. Camb. Philos. Soc. 39, 133–153 (1943)

    Article  MathSciNet  Google Scholar 

  2. Aronszajn, N.: Reproducing and pseudo-reproducing kernels and their application to the partial differential equations of physics. In: Studies in Partial Differential Equations. Technical report 5, preliminary note. Harvard University, Graduate School of Engineering, ii+31pp. (1948)

    Google Scholar 

  3. Aronszajn, N.: Theory of reproducing kernels. Trans. Am. Math. Soc. 68, 337–404 (1950)

    Article  MATH  MathSciNet  Google Scholar 

  4. Aronszajn, N.: Quadratic forms on vector spaces. In: Proceedings of the International Symposium on Linear Spaces, Jerusalem, pp. 29–87. Jerusalem Academic Press/Pergamon, Jerusalem/Oxford (1961)

    Google Scholar 

  5. Bergmann, S.: Über die Entwicklung der harmonische Funktionen der Ebene und des Raumes nach Orthogonalfunktionen. Math. Annalen 86, 238–271 (1922)

    Article  MATH  MathSciNet  Google Scholar 

  6. Berlinet, A., Thomas-Agnan, Ch.: Reproducing Kernel Hilbert Spaces in Probability and Statistics. Springer, Boston (2004)

    Book  MATH  Google Scholar 

  7. Bochner, S.: Vorlesungen über Fouriersche Integrale. Akademische Verlagsgesellschaft, Leipzig (1932)

    Google Scholar 

  8. Halmos, P.R.: A Hilbert Space Problem Book. D. van Nostrand Company, Toronto/London (1967)

    MATH  Google Scholar 

  9. Moore, E.H.: General Analysis. Memoirs of the American Philosophical Society, Part I, 1935, Part II, 1939. American Philosophical Society, Philadelphia (1935/1939)

    Google Scholar 

  10. Parthasarathy, K.R.: An Introduction to Quantum Stochastic Calculus. Birkhäuser, Basel (1992)

    Book  MATH  Google Scholar 

  11. Rochberg, R., Weaver, N.: Noncommutative complex analysis and Bargmann-Segal multipliers. Proc. Am. Math. Soc. 129, 2679–2687 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Rudin, W.: Real and Complex Analysis. McGraw-Hill, London (1970)

    Google Scholar 

  13. Saitoh, S.: Theory of Reproducing Kernels and Its Applications. Pitman Research Notes in Mathematics Series, vol. 189. Longman Scientific & Technical/Wiley, Harlow/New York (1988)

    Google Scholar 

  14. Saitoh, S.: Integral Transform, Reproducing Kernels and Their Application. CRC/Taylor and Francis Group (1997)

    Google Scholar 

  15. Shohat, J.A., Tamarkin, J.D.: The Problem of Moments. American Mathematical Society Colloquium Publications, vol. 15. American Mathematical Society, Providence (1943)

    Google Scholar 

  16. Simon, B.: The classical moment problem as a self-adjoint finite difference operator. Adv. Math. 137, 82–203 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  17. Szafraniec, F.H.: On the boundedness condition involved in dilation theory. Bull. Acad. Polon. Sci. Sér. sci. math. astr. et phys. 24, 877–881 (1976)

    MATH  MathSciNet  Google Scholar 

  18. Szafraniec, F.H.: Interpolation and domination by positive definite kernels. In: Andrean Cazacu, C., Boboc, N., Jurchescu, M., Suciu, I. (eds.) Complex Analysis – Fifth Romanian-Finish Seminar, Part 2, Proceedings, Bucarest, 1981. Lecture Notes in Mathematics, vol. 1014, pp. 291–295, Springer, Berlin/Heidelberg (1983)

    Google Scholar 

  19. Szafraniec, F.H.: The reproducing kernel Hilbert space and its multiplication operators. Oper. Theory Adv. Appl. 114, 253–263 (2000)

    MathSciNet  Google Scholar 

  20. Szafraniec, F.H.: Multipliers in the reproducing kernel Hilbert space, subnormality and noncommutative complex analysis. Oper. Theory Adv. Appl. 143, 313–331 (2003)

    MathSciNet  Google Scholar 

  21. Szafraniec, F.H.:, Przestrzenie Hilberta z ja̧drem reprodukuja̧cym (Hilbert Spaces with Reproducing Kernel, in Polish), Wydawnictwo Uniwersytetu Jagiellońskiego, Kraków (2004)

    Google Scholar 

  22. Szafraniec, F.H.: The reproducing kernel property and its space: more or less standard examples of applications. In: Alpay, D. (ed.) Operator Theory, chapter 2, pp. 31–58, Springer, Basel (2015). doi: 10.1007/978-3-0348-0692-3_70

    Chapter  Google Scholar 

  23. Zaremba, S.: L’équation biharmonique et une class remarquable de functions fondamentales harmoniques. Bulletin International de l’Académie des Sciences de Cracovie, Classe des Sciences Mathématiques et Naturelles, 147–196 (1907)

    Google Scholar 

Download references

Acknowledgements

The author was supported by the MNiSzW grant no. NN201 546438.

Author information

Authors and Affiliations

  1. Instytut Matematyki, Uniwersytet Jagielloński, Kraków, Poland

    Franciszek Hugon Szafraniec

Authors
  1. Franciszek Hugon Szafraniec
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Franciszek Hugon Szafraniec .

Editor information

Editors and Affiliations

  1. Earl Katz Chair in Algebraic System Theory, Department of Mathematics, Ben-Gurion University of the Negev, Be’er Sheva, Israel

    Daniel Alpay

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Basel

About this entry

Cite this entry

Szafraniec, F.H. (2015). The Reproducing Kernel Property and Its Space: The Basics. In: Alpay, D. (eds) Operator Theory. Springer, Basel. https://doi.org/10.1007/978-3-0348-0667-1_65

Download citation

Publish with us

Policies and ethics

Search

Navigation