Towards an Effectivisation of the Riemann Theorem
نویسنده
چکیده
LetQ be a connected and simply connected domain on the Riemann sphere, not coinciding with the Riemann sphere and with the whole complex plane C. Then, according to the Riemann Theorem, there exists a conformal bijection between Q and the exterior of the unit disk. In this paper we find an explicit form of this map for a broad class of domains with analytic boundaries. 2000 Math. Sabj. Class. 30C, 37K.
منابع مشابه
Effectivisation of a String Solution of the 2d Toda Hierarchy and the Riemann Theorem about Complex Domains
Let 0 ∈ D+ be a connected domain with analytic boundary on the complex plane C. Then according to the Riemann theorem there exists a function w(z) = 1 r z + ∑∞ j=0 pjz −j , mapping biholomorphically D− = C \D+ to the exterior of the unit disk {w ∈ C : |w| > 1}. From Wiegmann’s and Zabrodin’s rezults it follows that this function is described by the formula logw = log z − ∂t0( 1 2∂t0 + ∑ k>1 z−k...
متن کاملThe fuzzy generalized Taylor’s expansion with application in fractional differential equations
In this paper, the generalized Taylor’s expansion is presented for fuzzy-valued functions. To achieve this aim, fuzzyfractional mean value theorem for integral, and some properties of Caputo generalized Hukuhara derivative are necessarythat we prove them in details. In application, the fractional Euler’s method is derived for solving fuzzy fractionaldifferential equations in the sense of Caputo...
متن کاملExistence of positive solution to a class of boundary value problems of fractional differential equations
This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...
متن کاملBasic results on distributed order fractional hybrid differential equations with linear perturbations
In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...
متن کاملHigher order multi-point fractional boundary value problems with integral boundary conditions
In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...
متن کامل