Abstract
The Legendre transformation as a change of variables of convex functions is a familiar concept in physics. It was introduced into density functional theory by Lieb as a then completely new aspect of the transfer from v-dependences to n-dependences [Lieb, 1983]. Legendre transforms, or conjugate functionals in the modern terminology, are very powerful and very general tools of convex analysis [Zeidler, 1986, volume III, chapter 51] or [Young, 1969, §45]. This chapter introduces a few important mathematical concepts needed for handling conjugate functionals and thus provides a basis to understand the next chapter.
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© 1996 B. G. Teubner Verlagsgesellschaft Leipzig
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Eschrig, H. (1996). Legendre Transformation. In: The Fundamentals of Density Functional Theory. TEUBNER-TEXTE zur Physik, vol 32. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-97620-8_6
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DOI: https://doi.org/10.1007/978-3-322-97620-8_6
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-8154-3030-9
Online ISBN: 978-3-322-97620-8
eBook Packages: Springer Book Archive