Holomorphic methods in analysis and mathematical physics

نویسنده

  • Brian C. Hall
چکیده

Dedicated to my " father " Leonard Gross, and to the memory of my " grandfather " Irving Segal. Contents 1. Introduction 1 2. Basics of holomorphic function spaces 2 3. Examples of holomorphic function spaces 7 4. A special property of the Segal-Bargmann and weighted Bergman spaces 12 5. Canonical commutation relations 16 6. The Segal-Bargmann transform 21 7. Quantum mechanics and quantization 30 8. Toeplitz operators, anti-Wick ordering, and phase space probability densities 38 9. The Segal-Bargmann transform for compact Lie groups 44 10. To infinity and beyond 52 References 58

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Strictly Kähler-Berwald manifolds with constant‎ ‎holomorphic sectional curvature

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎. 

متن کامل

A remark on boundedness of composition operators between weighted spaces of holomorphic functions on the upper half-plane

In this paper, we obtain a sucient condition for boundedness of composition operators betweenweighted spaces of holomorphic functions on the upper half-plane whenever our weights are standardanalytic weights, but they don't necessarily satisfy any growth condition.

متن کامل

Szego Kernels and a Theorem of Tian

A variety of results in complex geometry and mathematical physics depend upon the analysis of holomorphic sections of high powers L⊗N of holomorphic line bundles L → M over compact Kähler manifolds ([A][Bis][Bis.V] [Bou.1][Bou.2][B.G][D][Don] [G][G.S][K][Ji] [T] [W]). The principal tools have been Hörmander’s L-estimate on the ∂̄-operator over M [T], the asymptotics of heat kernels kN (t, x, y) ...

متن کامل

Para-Kahler tangent bundles of constant para-holomorphic sectional curvature

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...

متن کامل

Composition operators between growth spaces‎ ‎on circular and strictly convex domains in complex Banach spaces‎

‎Let $\Omega_X$ be a bounded‎, ‎circular and strictly convex domain in a complex Banach space $X$‎, ‎and $\mathcal{H}(\Omega_X)$ be the space of all holomorphic functions from $\Omega_X$ to $\mathbb{C}$‎. ‎The growth space $\mathcal{A}^\nu(\Omega_X)$ consists of all $f\in\mathcal{H}(\Omega_X)$‎ ‎such that $$|f(x)|\leqslant C \nu(r_{\Omega_X}(x)),\quad x\in \Omega_X,$$‎ ‎for some constant $C>0$‎...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1999