## Conformal invariants in constructive theory of functions of complex variable |

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### Contents

General preliminary information | 1 |

Metrical properties of conformal map | 33 |

Polynomial approximations of | 71 |

Copyright | |

8 other sections not shown

### Common terms and phrases

A'-quasiconformal admissible continuum analogously analytical functions approximation of functions arbitrary point assume boundary prime ends Cauchy kernel Chapter compactum conformal mapping conformal radius Consequently consider constant continuity module Corollary curve family module curves separating Definition denote direct theorems domain G estimate Euclidean distance exterior Faber polynomials family of sections finite quasidisk formula fulfilled function f(z geometrical Green's formula harmonic harmonic polynomial homeomorphism IC-CI integral Jnk(t Jordan arc L-definition Laurent expansion Lebesgue measure Lemma level line locally-rectifiable notations obtain plane point zq polynomial approximation polynomial kernel polynomial Pn(z problem proof of Theorem properties prove quadrilateral quasiarc quasicircle quasiconformal mappings quasiconformality coefficient quasidisk G rectifiable rectifiable curves reduced module satisfies the inequality satisfies the relation satisfying the condition separate the points taking into account unit circle unit disk valid whence