scholarly journals Carleman Approximation on Totally Real Subsets of Class Ck.

1994 ◽  
Vol 74 ◽  
pp. 313 ◽  
Author(s):  
Manne Per E.
Keyword(s):  
Carleman Approximation ◽  
Totally Real

Carleman Approximation by Entire Functions on the Union of Two Totally Real Subspaces of Cn

1994 ◽  
Vol 37 (4) ◽  
pp. 522-526
Author(s):  
Per E. Manne
Keyword(s):  
Entire Functions ◽  
Continuous Functions ◽  
Real Dimension ◽  
Carleman Approximation ◽  
Polynomially Convex ◽  
Cauchy Riemann ◽  
Totally Real

AbstractLet L1, L2 ⊂ Cn be two totally real subspaces of real dimension n, and such that L1 ∩ L2 = {0}. We show that continuous functions on L1 ∪L2 allow Carleman approximation by entire functions if and only if L1 ∪L2 is polynomially convex. If the latter condition is satisfied, then a function f:L1 ∪L2 —> C such that f|LiCk(Li), i = 1,2, allows Carleman approximation of order k by entire functions if and only if f satisfies the Cauchy-Riemann equations up to order k at the origin.

A Characterization of Totally Real Carleman Sets and an Application to Products of Stratified Totally Real Sets

2016 ◽  
Vol 118 (2) ◽  
pp. 285 ◽  
Author(s):  
Benedikt S. Magnusson ◽  
Erlend Fornæss Wold
Keyword(s):  
Entire Functions ◽  
Carleman Approximation ◽  
Totally Real

We give a characterization of stratified totally real sets that admit Carleman approximation by entire functions. As an application we show that the product of two stratified totally real Carleman sets is a Carleman set.

scholarly journals Carleman approximation by holomorphic automorphisms of ℂ n

2018 ◽  
Vol 2018 (738) ◽  
pp. 131-148 ◽  
Author(s):  
Frank Kutzschebauch ◽  
Erlend Fornæss Wold
Keyword(s):  
Smooth Maps ◽  
Carleman Approximation ◽  
Totally Real ◽  
Holomorphic Automorphisms

Abstract We approximate smooth maps defined on non-compact totally real manifolds by holomorphic automorphisms of \mathbb{C}^{n} .

Curvature inequalities for C-totally real doubly warped products of locally conformal almost cosymplectic manifolds

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6449-6459 ◽  
Author(s):  
Akram Ali ◽  
Siraj Uddin ◽  
Wan Othman ◽  
Cenap Ozel
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Warped Products ◽  
Equality Case ◽  
Cosymplectic Manifolds ◽  
Almost Cosymplectic Manifold ◽  
Locally Conformal ◽  
Totally Real ◽  
Optimal Inequalities

In this paper, we establish some optimal inequalities for the squared mean curvature in terms warping functions of a C-totally real doubly warped product submanifold of a locally conformal almost cosymplectic manifold with a pointwise ?-sectional curvature c. The equality case in the statement of inequalities is also considered. Moreover, some applications of obtained results are derived.

The determination of units in totally real cubic fields

1960 ◽  
Vol 56 (4) ◽  
pp. 318-321 ◽  
Author(s):  
H. J. Godwin
Keyword(s):  
Trial And Error ◽  
Integral Lattice ◽  
Cubic Field ◽  
Cubic Fields ◽  
Trial And Error Method ◽  
Totally Real ◽  
Rational Integral ◽  
Fundamental Units ◽  
Error Method

The determination of a pair of fundamental units in a totally real cubic field involves two operations—finding a pair of independent units (i.e. such that neither is a power of the other) and from these a pair of fundamental units (i.e. a pair ε1; ε2 such that every unit of the field is of the form with rational integral m, n). The first operation may be accomplished by exploring regions of the integral lattice in which two conjugates are small or else by factorizing small primes and comparing different factorizations—a trial-and-error method, but often a quick one. The second operation is accomplished by obtaining inequalities which must be satisfied by a fundamental unit and its conjugates and finding whether or not a unit exists satisfying these inequalities. Recently Billevitch ((1), (2)) has given a method, of the nature of an extension of the first method mentioned above, which involves less work on the second operation but no less on the first.

Uniform approximation on totally real sets

1980 ◽  
Vol 253 (2) ◽  
pp. 139-144 ◽  
Author(s):  
Akira Sakai
Keyword(s):  
Uniform Approximation ◽  
Totally Real

Estimates for Kloosterman sums for totally real number fields

2001 ◽  
Vol 2001 (535) ◽  
Author(s):  
R. W. Bruggeman ◽  
R. J. Miatello ◽  
I. Pacharoni
Keyword(s):  
Real Number ◽  
Number Fields ◽  
Kloosterman Sums ◽  
Totally Real
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