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T(1) theorem

In mathematics, the T(1) theorem, first proved by, describes when an operator T given by a kernel can be extended to a bounded linear operator on the Hilbert space L2(Rn). [1]

9 relations: Adjoint, Annals of Mathematics, Bounded mean oscillation, Bounded operator, Distribution (mathematics), Hilbert space, Integral transform, Schwartz space, Springer Science+Business Media.

Adjoint

In mathematics, the term adjoint applies in several situations.

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Annals of Mathematics

The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study.

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Bounded mean oscillation

In harmonic analysis, a function of bounded mean oscillation, also known as a BMO function, is a real-valued function whose mean oscillation is bounded (finite).

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Bounded operator

In functional analysis, a branch of mathematics, a bounded linear operator is a linear transformation L between normed vector spaces X and Y for which the ratio of the norm of L(v) to that of v is bounded by the same number, over all non-zero vectors v in X. In other words, there exists some M > 0 such that for all v in X The smallest such M is called the operator norm \|L\|_ \, of L. A bounded linear operator is generally not a bounded function; the latter would require that the norm of L(v) be bounded for all v, which is not possible unless Y is the zero vector space.

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Distribution (mathematics)

Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.

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Hilbert space

The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.

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Integral transform

In mathematics, an integral transform is any transform T of the following form: The input of this transform is a function f, and the output is another function Tf.

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Schwartz space

In mathematics, Schwartz space is the function space of functions all of whose derivatives are rapidly decreasing.

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Springer Science+Business Media

Springer Science+Business Media or Springer is a global publishing company that publishes books, e-books and peer-reviewed journals in science, technical and medical (STM) publishing.

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T 1 theorem, T1 theorem.

References

[1] https://en.wikipedia.org/wiki/T(1)_theorem

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