## Complex Analysis, Functional Analysis and Approximation TheoryThis proceedings volume contains papers of research of expository nature, and is addressed to research workers and advanced graduate students in mathematics. Some of the papers are the written and expanded texts of lectures delivered at the conference, whereas others have been included by invitation. |

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### Contents

1 | |

25 | |

Metric projections of c onto closed vector sublattices | 47 |

A new theory of generalized functions | 57 |

The second dual of a JB triple system | 67 |

Holomorphic approximation in the theory of CauchyRiemann functions | 71 |

Approximation with subspaces of finite codimension | 83 |

Microhyperbolic analytic functions | 95 |

Normal solvability in duals of LFspaces | 173 |

A HahnBanach extension theorem for some holomorphic functions | 205 |

A glance at holomorphic factorization and uniform holomorphy | 221 |

Classification of LFspaces by some Bairelike covering properties | 247 |

Nonarchimedean gDFspaces and continuous functions | 261 |

Pseudoconvexity uconvexity and domains of uholomorphy | 273 |

The proof of the inversion mapping theorem in a Banach scale | 281 |

On certain metrizable locally convex spaces | 287 |

### Common terms and phrases

absolutely convex ANALYSIS AND APPROXIMATION analytic set APPROXIMATION THEORY Assume Baire—like Banach space barrelled bounded sets closed subspace codim codimension compact subset complex locally convex continuous linear continuous map continuous selection COROLLARY CR functions CR submanifold CS(E denote dense differential equations domain equivalent example exists F—convex finite dimensional follows Fréchet space Fredholm function f FUNCTIONAL ANALYSIS functional Hilbert space Hence Hilbert space holomorphic factorization holomorphic functions holomorphic map implies kernel Lemma Let f LF)—spaces linear mapping locally convex space LPDO manifold Math metrizable Mujica Editor n.a. gDF—space neighbourhood normed space open subset openness condition polynomial positive definite problem projective limit representation PROOF prove proximinal result satisfies the openness seminorm Separable Quotient sequence set of uniqueness sublattice surjective theorem tion topology totally real submanifold type zero uniform holomorphy vector space vector subspace