Tau Functions for the Dirac Operator on the Poincare Disk
نویسندگان
چکیده
In this paper we define tau functions for holonomic fields associated with the Dirac operator on the Poincare disk. The deformation analysis of the tau functions is worked out and in the case of the two point function, the tau function is expressed in terms of a Painleve function of type VI.
منابع مشابه
/ 93 09 01 7 v 1 2 S ep 1 99 3 Tau functions for the Dirac operator on the Poincaré disk
Table of Contents Introduction—1 §1 The Dirac operator on the Hyperbolic disk A covering of the frame bundle—4 The Dirac operator—7 Covariance of the Dirac operator—10 §2 Local Expansions Eigenfunctions for infinitesimal rotations—14 Differentiating local expansions with respect to the branch points—21 Estimates at infinity—24 §3 L 2 existence results A model for the simply connected covering D...
متن کاملInverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions
In this paper, we study the inverse problem for Dirac differential operators with discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...
متن کاملCertain subclasses of bi-univalent functions associated with the Aghalary-Ebadian-Wang operator
In this paper, we introduce and investigate two new subclasses of the functions class $ Sigma $ of bi-univalent functions defined in the open unit disk, which are associated with the Aghalary-Ebadian-Wang operator. We estimate the coefficients $|a_{2} |$ and $|a_{3} |$ for functions in these new subclasses. Several consequences of the result are also pointed out.
متن کاملSubordination and Superordination Properties for Convolution Operator
In present paper a certain convolution operator of analytic functions is defined. Moreover, subordination and superordination- preserving properties for a class of analytic operators defined on the space of normalized analytic functions in the open unit disk is obtained. We also apply this to obtain sandwich results and generalizations of some known results.
متن کاملProperties of multivalent functions associated with certain integral operator
Let A(p) denote the class of functions which are analytic in the open unit disk U. By making use of certain integral operator,we obtain some interesting properties of multivalent analytic functions.
متن کامل