Skip to main content

F-method for Matrix-Valued Differential Operators

  • 722 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 2170)

Abstract

In this chapter we recall from [14, 15, 21, 22] a method based on the Fourier transform (F-method) to find explicit formulæ of differential symmetry breaking operators. For our purpose we need to develop the F-method for matrix-valued operators. A new ingredient is a canonical decomposition of the algebraic Fourier transform of the vector-valued principal series representations into the “scalar part” involving differential operators of higher order and into the “vector part” of first order. This is formulated and proved in Sect. 3.4.

Keywords

  • Vector Bundle
  • Parabolic Subgroup
  • Weyl Algebra
  • Vector Part
  • Vector Bundle Versus

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   49.99
Price excludes VAT (Canada)
  • Compact, lightweight 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

Learn about institutional subscriptions

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

© 2016 Springer Nature Singapore Pte Ltd.

About this chapter

Cite this chapter

Kobayashi, T., Kubo, T., Pevzner, M. (2016). F-method for Matrix-Valued Differential Operators. In: Conformal Symmetry Breaking Operators for Differential Forms on Spheres. Lecture Notes in Mathematics, vol 2170. Springer, Singapore. https://doi.org/10.1007/978-981-10-2657-7_3

Download citation