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Schwartz Spaces and Zeta Integrals

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Zeta Integrals, Schwartz Spaces and Local Functional Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2228))

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Abstract

Throughout this chapter, we fix

  • a local field F of characteristic zero,

  • a split connected reductive F-group G,

  • an affine spherical embedding X+↪X satisfying Axiom 2.4.3,

  • relative invariants fi ∈ F[X] of eigencharacter ωi (Definition 2.4.2) for \(1 \leq i \leq r := \operatorname {rk}(\varLambda )\).

Hypothesis 4.6.4 will be made in the discussion of the L2-aspect, which serves to motivate the overall framework.

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Authors and Affiliations

  1. Beijing International Center for Mathematical Research, Peking University, Beijing, China

    Wen-Wei Li

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  1. Wen-Wei Li
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Li, WW. (2018). Schwartz Spaces and Zeta Integrals. In: Zeta Integrals, Schwartz Spaces and Local Functional Equations. Lecture Notes in Mathematics, vol 2228. Springer, Cham. https://doi.org/10.1007/978-3-030-01288-5_4

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