# H-derivative

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In mathematics, the ** H-derivative** is a notion of derivative in the study of abstract Wiener spaces and the Malliavin calculus.

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## Definition[edit]

Let be an abstract Wiener space, and suppose that is differentiable. Then the Fréchet derivative is a map

- ;

i.e., for , is an element of , the dual space to .

Therefore, define the **-derivative** at by

- ,

a continuous linear map on .

Define the **-gradient** by

- .

That is, if denotes the adjoint of , we have .

## See also[edit]

## References[edit]

**^**Victor Kac; Pokman Cheung (2002).*Quantum Calculus*. New York: Springer. pp. 80–84. ISBN 978-1-4613-0071-7.