Abstract
Recall that a second-order differential operator
is called elliptic if the quadratic form \(\sum {{a^{ij}}} \left( x \right){p_i}{p_j}\) is positive or negative definite for every x. More generally, recall that for a k-th order differential operator
the principal symbol σ(x, p) is the polynomial comprising the terms of highest degree, with the ∂ l replaced by iρ l (Chapter 24):
We say that A is elliptic if σ(x, p) vanishes only for p = 0.
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© 1993 Springer-Verlag Berlin Heidelberg
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Schwarz, A.S. (1993). Elliptic Operators. In: Quantum Field Theory and Topology. Grundlehren der mathematischen Wissenschaften, vol 307. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02943-5_28
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DOI: https://doi.org/10.1007/978-3-662-02943-5_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08130-9
Online ISBN: 978-3-662-02943-5
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