*Leon Ehrenpreis*

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198509783
- eISBN:
- 9780191709166
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509783.003.0008
- Subject:
- Mathematics, Mathematical Physics

This chapter deals with various questions which are related to the Radon transform, for example, the analog for forms, Selberg's trace formula. It gives a sharpening of the classical Euler-Maclaurin ...
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This chapter deals with various questions which are related to the Radon transform, for example, the analog for forms, Selberg's trace formula. It gives a sharpening of the classical Euler-Maclaurin sum formula — it is regarded here as a “truncated Poisson summation formula” and other truncations are introduced. The chapter suggests a “compact trick” which shows how to pass from compact to noncompact forms regarding the Plancherel formula.Less

This chapter deals with various questions which are related to the Radon transform, for example, the analog for forms, Selberg's trace formula. It gives a sharpening of the classical Euler-Maclaurin sum formula — it is regarded here as a “truncated Poisson summation formula” and other truncations are introduced. The chapter suggests a “compact trick” which shows how to pass from compact to noncompact forms regarding the Plancherel formula.

*Jean-Michel Bismut*

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691151298
- eISBN:
- 9781400840571
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691151298.003.0009
- Subject:
- Mathematics, Geometry / Topology

This chapter explicitly evaluates the Gaussian integral that appears in the right-hand side of a formula in Chapter 6 for the orbital integrals of the heat kernel, when γ is nonelliptic and ...
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This chapter explicitly evaluates the Gaussian integral that appears in the right-hand side of a formula in Chapter 6 for the orbital integrals of the heat kernel, when γ is nonelliptic and [t(γ),p₀] = 0. The computations here can be easily extended to the more general kernels considered in Chapter 6; the index formulas of Chapter 7 also play a key role here. This chapter begins by considering the case where G = K. It then computes explicitly the Gaussian integral when γ is nonelliptic and [t(γ),p₀] = 0. Finally, the chapter works out the case where G = SL₂(R).Less

This chapter explicitly evaluates the Gaussian integral that appears in the right-hand side of a formula in Chapter 6 for the orbital integrals of the heat kernel, when γ is nonelliptic and [**t**(γ),**p**₀] = 0. The computations here can be easily extended to the more general kernels considered in Chapter 6; the index formulas of Chapter 7 also play a key role here. This chapter begins by considering the case where *G* = *K*. It then computes explicitly the Gaussian integral when γ is nonelliptic and [**t**(γ),**p**₀] = 0. Finally, the chapter works out the case where *G* = SL₂(**R**).