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searching for Legendre transform (integral transform) 4 found (7 total)

alternate case: legendre transform (integral transform)

Beltrami identity (1,076 words) [view diff] no match in snippet view article find links to article

closed-form solution is often very difficult to obtain. Thus, the Legendre transform of the Lagrangian, the Hamiltonian, is constant along the dynamical

Inverse function rule (1,789 words) [view diff] no match in snippet view article find links to article

is also of interest, as it is used in showing the convexity of the Legendre transform. Let z = f ′ ( x ) {\displaystyle z=f'(x)} then we have, assuming

Convolution (8,819 words) [view diff] no match in snippet view article find links to article

with the role of the Fourier transform is played instead by the Legendre transform: φ ∗ ( x ) = sup y ( x ⋅ y − φ ( y ) ) . {\displaystyle \varphi ^{*}(x)=\sup

Calculus of variations (9,530 words) [view diff] no match in snippet view article find links to article

conserved quantity. In this case, this quantity is the Hamiltonian, the Legendre transform of the Lagrangian, which (often) coincides with the energy of the