A spectral decomposition of orbital integrals for <Emphasis Type='Italic'>PGL</Emphasis>(2,? <Emphasis Type='Italic'>F</Emphasis>) (with an appendix by S. Debacker)

David Kazhdan

摘要

AbstractLetFbe a local non-archimedian field,Ga semisimpleF-group,dga Haar measure onGand$$mathcal {S}(G)$$

S (G)

be the space of locally constant complex valued functionsfonGwith compact support. For any regular elliptic congugacy class$$Omega =h^Gsubset G$$

Ω = h^{G} ? G

we denote by$$I_Omega $$

I_{Ω}

theG-invariant functional on$$mathcal {S}(G)$$

S (G)

given by$$egin{aligned} I_Omega (f)=int _G f(g^{-1}hg)dg end{aligned}$$

\begin{matrix} I_{Ω} (f) = \int_{G} f (g^{- 1} h g) d g \end{matrix}

This paper provides the spectral decomposition of functionals$$I_Omega $$

I_{Ω}

in the case

机译：<！[cdata [ <标题>抽象 ara id =“par1”> let <重点类型=“斜体”> f < /重点>是一个本地非Archimedian字段，<重点类型=“斜体”> g 半单一<重点类型=“斜体”> f -group，<重点类型=“italic”> DG <重点类型=“斜体”> G 和 $$ mathcal {s}（g）$$

s（g）是局部恒定复数函数的空间<重点键入=“斜体”> f<重点类型=“斜体”> g，支持紧凑的支持。对于任何常规的椭圆委员会$$  oomega = h ^ g  subset g $$ ω=HG？g我们表示$$ I_  Omega $$ iωG -Invarian t函数在 < arequationsource格式=“tex”> $$  mathcal {s}（g）$$ s（g）< / mo>由<等式ID =“equ1”给出>$$  begined {对齐} i_  oomega（f）=  int _g f（g ^ { -  1} HG）DG  End {对齐} $$ < MROW> \begin{matrix} I \end{matrix}

A spectral decomposition of orbital integrals for PGL(2,? F) (with an appendix by S. Debacker)

摘要

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