Symbol of a Differential Operator
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Symbol of a Differential Operator

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the symbol of a linear differential operator associates to a differential operator a polynomial by, roughly speaking, replacing each partial derivative by a new variable. The symbol of a differential operator has broad applications to Fourier analysis. In particular, in this connection it leads to the notion of a pseudo-differential operator. The highest-order terms of the symbol, known as the principal symbol, almost completely controls the qualitativ...