The Cauchy Harish-chandra Integral, for the Pair
نویسنده
چکیده
One of the main problems in the theory of dual pairs is the description of the correspondence of characters of representations in Howe duality, [H]. In [D-P] a formula describing this correspondence was obtained under some very strong assumptions. In [P] the second author has developed a notion of a Cauchy Harish-Chandra integral for any real reductive pair, in order to describe this correspondence of characters. In this paper a special case of this integral will be studied. The results obtained here are crucial for the estimates needed in [P]. (See the proof of Theorem 10.19, page 343, in [P].)
منابع مشابه
GENERALIZED HARISH-CHANDRA MODULES WITH GENERIC MINIMAL k-TYPE
We make a first step towards a classification of simple generalized Harish-Chandra modules which are not Harish-Chandra modules or weight modules of finite type. For an arbitrary algebraic reductive pair of complex Lie algebras (g, k), we construct, via cohomological induction, the fundamental series F ·(p, E) of generalized Harish-Chandra modules. We then use F ·(p, E) to characterize any simp...
متن کاملTo the memory of Armand Borel GENERALIZED HARISH-CHANDRA MODULES WITH GENERIC MINIMAL k-TYPE
We make a first step towards a classification of simple generalized HarishChandra modules which are not Harish-Chandra modules or weight modules of finite type. For an arbitrary algebraic reductive pair of complex Lie algebras (g, k), we construct, via cohomological induction, the fundamental series F ·(p, E) of generalized Harish-Chandra modules. We then use F ·(p, E) to characterize any simpl...
متن کاملAn effective method for approximating the solution of singular integral equations with Cauchy kernel type
In present paper, a numerical approach for solving Cauchy type singular integral equations is discussed. Lagrange interpolation with Gauss Legendre quadrature nodes and Taylor series expansion are utilized to reduce the computation of integral equations into some algebraic equations. Finally, five examples with exact solution are given to show efficiency and applicability of the method. Also, w...
متن کاملExistence of Mild Solutions to a Cauchy Problem Presented by Fractional Evolution Equation with an Integral Initial Condition
In this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional Cauchy problem with an integral initial condition in Banach spaces.
متن کامل$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework
In the present work the space $L_{p;r} $ which is continuously embedded into $L_{p} $ is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007