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T(1) theorem

Index 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 in mathematics, 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 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 above by the same number, over all non-zero vectors v in X. In other words, there exists some M\ge 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 L(v).

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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 maps an equation from its original domain into another domain where it might be manipulated and solved much more easily than in the original domain.

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Schwartz space

In mathematics, Schwartz space is the function space of all functions whose derivatives are rapidly decreasing (defined rigorously below).

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, 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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