Skip to main content

Selfadjoint extension of the Casimir operator

  • Chapter
  • 429 Accesses

Part of the Modern Birkhäuser Classics book series

Abstract

In 1.2.6 and 1.5.7 we discussed the selfadjoint extension of the differential operator L r . This concerned the modular case. The extension was an operator in a Hilbert space H(r) for r ∈ ℝ. Its eigenfunctions were stated to be modular forms, and \(\frac{{|r|}}{2}\left( {1 - \frac{{|r|}}{2}} \right)\) its smallest eigenvalue. In this chapter we prove these statements, in the more general setting of Part I. We work in a Hilbert space H(x,l) depending on a unitary character x of \(\widetilde \Gamma \), and a (real) weight l suitable for x. In Section 6.1 we define this Hilbert space as a completion of the space of all smooth x-l-equivariant functions with compact support in Y.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-0346-0336-2_6
  • Chapter length: 21 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   84.99
Price excludes VAT (USA)
  • ISBN: 978-3-0346-0336-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   109.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1994 Springer Basel AG

About this chapter

Cite this chapter

Bruggeman, R.W. (1994). Selfadjoint extension of the Casimir operator. In: Families of Automorphic Forms. Modern Birkhäuser Classics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0346-0336-2_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-0346-0336-2_6

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0346-0335-5

  • Online ISBN: 978-3-0346-0336-2

  • eBook Packages: Springer Book Archive