Titlebook: Notions of Convexity; Lars Hörmander Book 19941st edition Birkhäuser Boston 1994 Complex analysis.Convexity.Differential operator.Mathemat

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it seems to be extremely important to impart solid knowledge with regard to the differences between the national education systems, even if tacitly more ‘unity’ is its ultimate aim: we must know the differences and their roots before we can create more unity.

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Convex Functions of One Variable,qualities in analysis by convexity arguments. The Legendre transform (conjugate convex functions) is discussed in Section 1.3 in a spirit which prepares for the case of several variables in Chapter II. Section 1.4 is an interlude presenting an interesting characterization of the Γ function by the fu

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Convexity in a Finite-Dimensional Vector Space,tions. It ends with some convexity properties of hyperbolic polynomials which will be important in Section 2.3. The Legendre transformation is extended to several variables in Section 2.2, where we also give some applications to game theory and linear programming. The role of the Legendre transforma

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Subharmonic Functions,harmonic functions. However, this requires some background knowledge concerning harmonic functions which is provided in Section 3.1. Basic facts concerning subharmonic functions are then given in Section 3.2, mainly by means of the mean value property and the characterization as distributions with p

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Plurisubharmonic Functions,ature compared to the parallel Section 3.2 is that there is a class of associated pseudo-convex sets which have the same relation to plurisubharmonic functions as convex sets have to convex functions. In Section 4.2 existence theorems for the Cauchy-Riemann equations in several complex variables are

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Convexity with Respect to a Linear Group,e full linear group, the orthogonal group and the full complex linear group. We have also seen that the set of subharmonic functions invariant under the full (complex) linear group consists of convex (plurisubharmonic functions). In this chapter we shall consider the spaces of functions attached sim

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Anal-Canal

,Convexity and Condition (.Ψ),y pseudo-convex domain. This may seem like a very special problem, but in fact, via the transformation theory of microlocal analysis, it is equivalent to the central question of local solvability for microfunctions. This transformation theory is beyond the scope of these lectures, but we shall discu

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ng pregnant in schools are not re-entering school despite the re-entry policy having been in place since 1997. The objectives of this chapter are to explore the challenges faced by teenage mothers and the current support systems in secondary schools. The chapter is based on teenage mother’s pregnanc