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- Symbol_of_a_differential_operator abstract "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 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 characteristics of the partial differential equation. Consequently, the symbol is often fundamental for the solution of such equations, and is one of the main computational devices used to study their singularities.".
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- Symbol_of_a_differential_operator wikiPageWikiLink Atiyah–Singer_index_theorem.
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- Symbol_of_a_differential_operator wikiPageWikiLink Category:Differential_operators.
- Symbol_of_a_differential_operator wikiPageWikiLink Category:Vector_bundles.
- Symbol_of_a_differential_operator wikiPageWikiLink Closed_manifold.
- Symbol_of_a_differential_operator wikiPageWikiLink Cotangent_bundle.
- Symbol_of_a_differential_operator wikiPageWikiLink Differential_operator.
- Symbol_of_a_differential_operator wikiPageWikiLink Elliptic_operator.
- Symbol_of_a_differential_operator wikiPageWikiLink Elliptic_partial_differential_equation.
- Symbol_of_a_differential_operator wikiPageWikiLink Euclidean_space.
- Symbol_of_a_differential_operator wikiPageWikiLink Fourier_analysis.
- Symbol_of_a_differential_operator wikiPageWikiLink Fourier_transform.
- Symbol_of_a_differential_operator wikiPageWikiLink Fredholm_operator.
- Symbol_of_a_differential_operator wikiPageWikiLink Homogeneous_polynomial.
- Symbol_of_a_differential_operator wikiPageWikiLink Hyperbolic_partial_differential_equation.
- Symbol_of_a_differential_operator wikiPageWikiLink Kernel_(algebra).
- Symbol_of_a_differential_operator wikiPageWikiLink Local_coordinates.
- Symbol_of_a_differential_operator wikiPageWikiLink Mathematics.
- Symbol_of_a_differential_operator wikiPageWikiLink Method_of_characteristics.
- Symbol_of_a_differential_operator wikiPageWikiLink Multi-index_notation.
- Symbol_of_a_differential_operator wikiPageWikiLink Multiplier_(Fourier_analysis).
- Symbol_of_a_differential_operator wikiPageWikiLink Parabolic_partial_differential_equation.
- Symbol_of_a_differential_operator wikiPageWikiLink Partial_derivative.
- Symbol_of_a_differential_operator wikiPageWikiLink Partial_differential_equation.
- Symbol_of_a_differential_operator wikiPageWikiLink Polynomial.
- Symbol_of_a_differential_operator wikiPageWikiLink Pseudo-differential_operator.
- Symbol_of_a_differential_operator wikiPageWikiLink Schwartz_space.
- Symbol_of_a_differential_operator wikiPageWikiLink Symmetric_algebra.
- Symbol_of_a_differential_operator wikiPageWikiLink Symmetric_tensor.
- Symbol_of_a_differential_operator wikiPageWikiLink Tensor.
- Symbol_of_a_differential_operator wikiPageWikiLink Tensor_product.
- Symbol_of_a_differential_operator wikiPageWikiLink Vector_bundle.
- Symbol_of_a_differential_operator wikiPageWikiLinkText "Symbol of a differential operator".
- Symbol_of_a_differential_operator wikiPageWikiLinkText "leading symbol".
- Symbol_of_a_differential_operator wikiPageWikiLinkText "principal symbol".
- Symbol_of_a_differential_operator wikiPageWikiLinkText "standard symbol".
- Symbol_of_a_differential_operator wikiPageWikiLinkText "symbol of a differential operator".
- Symbol_of_a_differential_operator wikiPageWikiLinkText "symbol".
- Symbol_of_a_differential_operator wikiPageWikiLinkText "symbols".
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- Symbol_of_a_differential_operator wikiPageUsesTemplate Template:Expert-subject.
- Symbol_of_a_differential_operator wikiPageUsesTemplate Template:Reflist.
- Symbol_of_a_differential_operator subject Category:Differential_operators.
- Symbol_of_a_differential_operator subject Category:Vector_bundles.
- Symbol_of_a_differential_operator type Bundle.
- Symbol_of_a_differential_operator comment "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.".
- Symbol_of_a_differential_operator label "Symbol of a differential operator".
- Symbol_of_a_differential_operator sameAs Q4555178.
- Symbol_of_a_differential_operator sameAs 微分作用素の表象.
- Symbol_of_a_differential_operator sameAs 주표상.
- Symbol_of_a_differential_operator sameAs m.02qkyb6.
- Symbol_of_a_differential_operator sameAs Q4555178.
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- Symbol_of_a_differential_operator isPrimaryTopicOf Symbol_of_a_differential_operator.