Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Singular Integrals and the Principal Series, IV.

A W Knapp1, E M Stein

  • 1Department of Mathematics, Cornell University, Ithaca, New York 14853.

Proceedings of the National Academy of Sciences of the United States of America
|June 1, 1975
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

The skeletal consequences of epidural steroid injections: a literature review.

Osteoporosis international : a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA·2021
Same author

Risk factors for multi-joint disease in patients with glucocorticoid-induced osteonecrosis.

Osteoporosis international : a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA·2021
Same author

Low volumetric bone density is a risk factor for early complications after spine fusion surgery.

Osteoporosis international : a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA·2020
Same author

Disrupted radial and tibial microarchitecture in patients with monoclonal gammopathy of undetermined significance.

Osteoporosis international : a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA·2018
Same author

Abnormal microarchitecture and stiffness in postmenopausal women using chronic inhaled glucocorticoids.

Osteoporosis international : a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA·2018
Same author

What is the clinical significance of esophagogastric junction outflow obstruction? evaluation of 60 patients at a tertiary referral center.

Neurogastroenterology and motility·2017
Same journal

Chemotactic self-organization captures the dynamics of mammalian hair follicle patterning.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Tomographic imaging of superconducting order using particle-hole interference.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Inhibitory potential of autologous neutralizing antibodies sets quantitative limits on the rebound-competent HIV-1 reservoir.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Inferring epidemiological parameters under an infectious phylogeography model with visitor dynamics.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Analytical modeling for suction cup designs for skin-interfaced wearable devices.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Improving cell-free metabolism through direct integration of artificial respiratory chains.

Proceedings of the National Academy of Sciences of the United States of America·2026
See all related articles

Researchers normalized intertwining operators for unitary representations of real semisimple Lie groups. This yields dimension formulas for commuting algebras and establishes complementary series, extending previous findings.

Area of Science:

  • Representation theory
  • Harmonic analysis
  • Lie group theory

Background:

  • Unitary representations are fundamental in understanding Lie groups.
  • The Plancherel formula decomposes representations.
  • Intertwining operators are crucial for relating representations.

Purpose of the Study:

  • To introduce a new normalization for intertwining operators.
  • To derive dimension formulas for commuting algebras of unitary representations.
  • To prove the existence of new complementary series.

Main Methods:

  • Construction and normalization of intertwining operators.
  • Application of operators to derive dimension formulas.
  • Utilizing operator properties to establish complementary series existence.

Related Experiment Videos

Main Results:

  • New dimension formulas for commuting algebras of unitary representations.
  • Existence of complementary series analogous to those of principal series.
  • A unified approach to studying unitary representations.

Conclusions:

  • The normalized intertwining operators provide powerful tools for representation theory.
  • The findings deepen the understanding of unitary representations and complementary series.
  • This work offers a foundation for further research in Lie group representation theory.