# Harmonic analysis on semisimple Lie groups

@article{HarishChandra1970HarmonicAO, title={Harmonic analysis on semisimple Lie groups}, author={Harish-Chandra}, journal={Bulletin of the American Mathematical Society}, year={1970}, volume={76}, pages={529-551} }

Then tr 4̂ is actually independent of the choice of this base. Let VT denote the set of a l l /G^ i (G) such that ir(f) is of the trace class. Then Vr is a linear subspace of Li(G). Put 0 . ( / ) = tr *•(ƒ) ( f £ F T ) . Then ®T is a linear function on VT which we may call the character of 7T. Of course this concept would be useful only when the space V* is fairly large. Let 8(G) denote the set of all equivalence classes of irreducible unitary representations of G. It is easy to see that for…

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## References

SHOWING 1-10 OF 12 REFERENCES

Automorphic Forms on Semisimple Lie Groups

- Mathematics
- 1968

A solution to get the problem off, have you found it? Really? What kind of solution do you resolve the problem? From what sources? Well, there are so many questions that we utter every day. No matter…

Théorie des distributions

- Mathematics
- 1966

II. Differentiation II.2. Examples of differentiation. The case of one variable (n = 1). II.2.3. Pseudofunctions. Hadamard finite part. We calculate the derivative of a function f(x) which is equal…

Groupes Réductifs

- 1965

© Publications mathématiques de l’I.H.É.S., 1965, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…

Decomposition of unitary representations de ned by a discrete subgroup of nilpotent groups

- Mathematics
- 1965

Characters of the discrete series of representations of sl(2) over a local field.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1968

Infinite - dimensional group representations , Bull

- Amer . Math . Soc .