Symbol of a differential operator
In mathematics, the symbol of a linear differential operator is a polynomial representing a differential operator, which is obtained, roughly speaking, by 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 qualitative behavior of solutions of a partial differential equation. Linear elliptic partial differential equations can be characterized as those whose principal symbol is nowhere zero. In the study of hyperbolic and parabolic partial differential equations, zeros of the principal symbol correspond to the character
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Symbol of a differential operator
In mathematics, the symbol of a linear differential operator is a polynomial representing a differential operator, which is obtained, roughly speaking, by 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 qualitative behavior of solutions of a partial differential equation. Linear elliptic partial differential equations can be characterized as those whose principal symbol is nowhere zero. In the study of hyperbolic and parabolic partial differential equations, zeros of the principal symbol correspond to the character
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En mathématiques, le symbole d ...... els, d'opérateur elliptique...
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In mathematics, the symbol of ...... to study their singularities.
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数学の分野における微分作用素の表象(びぶんさようそのひょうし ...... 解の特異性を調べる上で用いられる主要な道具の内の一つである。
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En mathématiques, le symbole d ...... opérateur pseudo-différentiel.
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In mathematics, the symbol of ...... ol correspond to the character
@en
数学の分野における微分作用素の表象(びぶんさようそのひょうし ...... 解の特異性を調べる上で用いられる主要な道具の内の一つである。
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Symbol of a differential operator
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Symbole d'un opérateur différentiel
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微分作用素の表象
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주표상
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