In this paper, we give a method which aUows us to construct a class of Parseval frames for L2（R） from Fourier frame for L2（X）. The result shows that the function which generates a Oabor frame by translations and m...In this paper, we give a method which aUows us to construct a class of Parseval frames for L2（R） from Fourier frame for L2（X）. The result shows that the function which generates a Oabor frame by translations and modulations has ＂good＂ properties, i.e., it is suifficiently smooth and compactly supported.展开更多
According to a program of Braverman, Kazhdan and NgS, for a large class of split unramified reductive groups G and representations p of the dual group G, the unramified local L-factor L（s, π, ρ） can be expressed a...According to a program of Braverman, Kazhdan and NgS, for a large class of split unramified reductive groups G and representations p of the dual group G, the unramified local L-factor L（s, π, ρ） can be expressed as the trace of π（fρ,s） for a function fρ,s with non-compact support whenever Re（s） ≥ 0. Such a function should have useful interpretations in terms of geometry or eombinatories, and it can be plugged into the trace formula to study certain sums of automorphic L-functions. It also fits into the conjectural framework of Schwartz spaces for reductive monoids due to Sakellaridis, who coined the term basic functions; this is supposed to lead to a generalized Tamagawa-Godement-Jaequet theory for （G, ρ）. In this paper, we derive some basic properties for the basic functions fρ,s and interpret them via invariant theory. In particular, their coefficients are interpreted as certain generalized Kostka-Foulkes polynomials defined by Panyushev. These coefficients can be encoded into a rational generating function.展开更多
基金Supported by Henan Province Education Department Natural Science Foundation of China（2008B510001）
文摘In this paper, we give a method which aUows us to construct a class of Parseval frames for L2（R） from Fourier frame for L2（X）. The result shows that the function which generates a Oabor frame by translations and modulations has ＂good＂ properties, i.e., it is suifficiently smooth and compactly supported.
文摘According to a program of Braverman, Kazhdan and NgS, for a large class of split unramified reductive groups G and representations p of the dual group G, the unramified local L-factor L（s, π, ρ） can be expressed as the trace of π（fρ,s） for a function fρ,s with non-compact support whenever Re（s） ≥ 0. Such a function should have useful interpretations in terms of geometry or eombinatories, and it can be plugged into the trace formula to study certain sums of automorphic L-functions. It also fits into the conjectural framework of Schwartz spaces for reductive monoids due to Sakellaridis, who coined the term basic functions; this is supposed to lead to a generalized Tamagawa-Godement-Jaequet theory for （G, ρ）. In this paper, we derive some basic properties for the basic functions fρ,s and interpret them via invariant theory. In particular, their coefficients are interpreted as certain generalized Kostka-Foulkes polynomials defined by Panyushev. These coefficients can be encoded into a rational generating function.
