Distribution (mathematics) - Using Holomorphic Functions As Test Functions

Using Holomorphic Functions As Test Functions

The success of the theory led to investigation of the idea of hyperfunction, in which spaces of holomorphic functions are used as test functions. A refined theory has been developed, in particular Mikio Sato's algebraic analysis, using sheaf theory and several complex variables. This extends the range of symbolic methods that can be made into rigorous mathematics, for example Feynman integrals.

Read more about this topic:  Distribution (mathematics)

Famous quotes containing the words functions and/or test:

    Let us stop being afraid. Of our own thoughts, our own minds. Of madness, our own or others’. Stop being afraid of the mind itself, its astonishing functions and fandangos, its complications and simplifications, the wonderful operation of its machinery—more wonderful because it is not machinery at all or predictable.
    Kate Millett (b. 1934)

    There is held to be no surer test of civilisation than the increase per head of the consumption of alcohol and tobacco. Yet alcohol and tobacco are recognisable poisons, so that their consumption has only to be carried far enough to destroy civilisation altogether.
    Havelock Ellis (1859–1939)