Schwartz Space - Examples of Functions in The Schwartz Space

Examples of Functions in The Schwartz Space

  • If i is a multi-index, and a is a positive real number, then
  • Any smooth function f with compact support is in S(Rn). This is clear since any derivative of f is continuous and supported in the support of f, so (xαDβ) f has a maximum in Rn by the extreme value theorem.

Read more about this topic:  Schwartz Space

Famous quotes containing the words examples of, examples, functions and/or space:

    Histories are more full of examples of the fidelity of dogs than of friends.
    Alexander Pope (1688–1744)

    There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.
    Bernard Mandeville (1670–1733)

    Adolescents, for all their self-involvement, are emerging from the self-centeredness of childhood. Their perception of other people has more depth. They are better equipped at appreciating others’ reasons for action, or the basis of others’ emotions. But this maturity functions in a piecemeal fashion. They show more understanding of their friends, but not of their teachers.
    Terri Apter (20th century)

    Through space the universe encompasses and swallows me up like an atom; through thought I comprehend the world.
    Blaise Pascal (1623–1662)