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The Fréchet space of smooth functions whose derivatives decay faster than every inverse polynomial.
wp-schwartz_spacenlab-schwartz_spaceEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Schwartz functions form a Fréchet space with seminorms controlling all polynomially weighted derivatives.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-schwartz_spacenlab-schwartz_spaceEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Tempered distributions are continuous linear functionals on Schwartz space.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-distribution_spacenlab-distribution_spaceThis is an authored directed relation from the source endpoint to the target endpoint.
The Fourier transform is a canonical automorphism of Schwartz space and extends, with additional structure, to functions and tempered distributions.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-fourier_transformnlab-fourier_transformThis is an authored directed relation from the source endpoint to the target endpoint.
Quantum fields are smeared against smooth test functions, often Schwartz functions in Minkowski-space treatments.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
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