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Longer titles found: Unbounded operator (view)

searching for Bounded operator 29 found (114 total)

Dilation (operator theory) (678 words) [view diff] exact match in snippet view article

formally, let T be a bounded operator on some Hilbert space H, and H be a subspace of a larger Hilbert space H' . A bounded operator V on H' is a dilation

Hilbert's inequality (663 words) [view diff] exact match in snippet view article find links to article

by Issai Schur. It implies that the discrete Hilbert transform is a bounded operator in ℓ2. Let (um) be a sequence of complex numbers. If the sequence is

Fourier integral operator (681 words) [view diff] exact match in snippet view article find links to article

order zero, it is possible to show that T {\displaystyle T} defines a bounded operator from L 2 {\displaystyle L^{2}} to L 2 {\displaystyle L^{2}} . One motivation

Brezis–Gallouët inequality (1,004 words) [view diff] exact match in snippet view article find links to article

)\to H^{2}(\mathbb {R} ^{2})} such that: P {\displaystyle P} is a bounded operator from H 1 ( Ω ) {\displaystyle H^{1}(\Omega )} to H 1 ( R 2 ) {\displaystyle

Spectrum (946 words) [view diff] exact match in snippet view article find links to article

the matrix. In functional analysis, the concept of the spectrum of a bounded operator is a generalization of the eigenvalue concept for matrices. In algebraic

Christ–Kiselev maximal inequality (628 words) [view diff] exact match in snippet view article find links to article

N , ν ) {\displaystyle T^{*}:L^{p}(M,\mu )\to L^{q}(N,\nu )} is a bounded operator, and ‖ T ∗ f ‖ q ≤ 2 − ( p − 1 − q − 1 ) ( 1 − 2 − ( p − 1 − q − 1

Regularization by spectral filtering (2,234 words) [view diff] exact match in snippet view article find links to article

regularization amounts to substituting the original operator by a bounded operator called the "regularization operator" that has a condition number controlled

Singular integral operators of convolution type (12,876 words) [view diff] exact match in snippet view article find links to article

projection P of L2(T) onto H2(T) is called the Szegő projection. It is a bounded operator on L2(T) with operator norm 1. By Cauchy's integral formula, F ( z

Normal matrix (1,657 words) [view diff] exact match in snippet view article find links to article

normal operators on infinite-dimensional Hilbert spaces. For example, a bounded operator satisfying (9) is only quasinormal. It is occasionally useful (but

Toeplitz operator (547 words) [view diff] exact match in snippet view article find links to article

{\displaystyle T_{g}=PM_{g}\vert _{H^{2}},} where " | " means restriction. A bounded operator on H 2 {\displaystyle H^{2}} is Toeplitz if and only if its matrix

Singular trace (3,733 words) [view diff] exact match in snippet view article find links to article

Calkin sequence space j. In particular, if a bounded operator A belongs to J whenever there is a bounded operator B in J such that for every natural number

Jordan normal form (6,956 words) [view diff] exact match in snippet view article find links to article

The holomorphic functional calculus is defined as follows: Fix a bounded operator T. Consider the family Hol(T) of complex functions that is holomorphic

Marcel Riesz (1,310 words) [view diff] exact match in snippet view article find links to article

devised an interpolation theorem to show that the Hilbert transform is a bounded operator in Lp (1 < p < ∞). The generalisation of the interpolation theorem

Calkin correspondence (753 words) [view diff] exact match in snippet view article find links to article

orthonormal basis {en }n=0∞. Associate to a sequence a from j the bounded operator d i a g ( a ) = ∑ n = 0 ∞ a n | e n ⟩ ⟨ e n | , {\displaystyle {\rm

Hundred-dollar, Hundred-digit Challenge problems (914 words) [view diff] exact match in snippet view article find links to article

a_{12}=1/2,a_{21}=1/3,a_{13}=1/4,a_{22}=1/5,a_{31}=1/6,\dots } is a bounded operator on ℓ 2 {\displaystyle \ell ^{2}} . What is | | A | | {\displaystyle

Schatten norm (1,142 words) [view diff] exact match in snippet view article find links to article

{\displaystyle H_{2}} be Hilbert spaces, and T {\displaystyle T} a (linear) bounded operator from H 1 {\displaystyle H_{1}} to H 2 {\displaystyle H_{2}} . For p

KK-theory (1,098 words) [view diff] exact match in snippet view article find links to article

of A on H as even bounded operators that commute with B, and F is a bounded operator on H of degree 1, which again commutes with B. They are required to

Positive-definite function on a group (1,586 words) [view diff] exact match in snippet view article find links to article

) = T n {\displaystyle F(n)=T^{n}} where T {\displaystyle T} is a bounded operator acting on some Hilbert space. One can show that the kernel K ( n ,

William F. Donoghue Jr. (563 words) [view diff] exact match in snippet view article find links to article

7.1031. Donoghue, William F. (1957). "On the numerical range of a bounded operator". The Michigan Mathematical Journal. 4 (3): 261–263. doi:10.1307/mmj/1028997958

Regularity structure (894 words) [view diff] exact match in snippet view article find links to article

assigns to any two points x {\displaystyle x} and y {\displaystyle y} a bounded operator Γ x y {\displaystyle \Gamma _{xy}} , which has the role of converting

Symmetrizable compact operator (1,384 words) [view diff] exact match in snippet view article find links to article

sum is not orthogonal the restriction PNK*PN of K* is similar by a bounded operator with bounded inverse to the diagonal operator on the orthogonal direct

Singular integral operators on closed curves (5,032 words) [view diff] exact match in snippet view article find links to article

projection P of L2(T) onto H2(T) is called the Szegő projection. It is a bounded operator on L2(T) with operator norm 1. By Cauchy's theorem F ( z ) = 1 2 π

Neumann–Poincaré operator (11,017 words) [view diff] exact match in snippet view article find links to article

functions, it is not a bounded operator on L2(∂Ω). In fact it is a pseudodifferential operator of order 1, so does define a bounded operator between Sobolev

Muckenhoupt weights (1,674 words) [view diff] exact match in snippet view article find links to article

}K\right|\leq C|x|^{-n-\alpha }.} Then, for each 1 < p < ∞ and ω ∈ Ap, T is a bounded operator on Lp(ω(x)dx). That is, we have the estimate ∫ | T ( f ) ( x ) | p

Rayleigh–Ritz method (5,817 words) [view diff] exact match in snippet view article find links to article

"Method of orthogonal projections and approximation of the spectrum of a bounded operator". Studia Mathematica. 65: 21–29. doi:10.4064/sm-65-1-21-29. Bögli,

Uniformly bounded representation (3,535 words) [view diff] exact match in snippet view article find links to article

word length on F2 for a given set of generators a, b. Let T be the bounded operator defined on basis elements by T e 1 = 0 , T e g = e g ′ , {\displaystyle

Grunsky matrix (6,334 words) [view diff] exact match in snippet view article find links to article

(z-w)^{2}}\,dx\,dy.} For any bounded open region Ω in C it defines a bounded operator TΩ from the conjugate of the Bergman space of Ω onto the Bergman space

Translation operator (quantum mechanics) (6,344 words) [view diff] exact match in snippet view article

unitary operator. First, it must shown that translation operator is a bounded operator. It is sufficient to state that for all ψ ∈ L 2 ( [ a , b ] , μ ) {\displaystyle

Glossary of real and complex analysis (4,340 words) [view diff] exact match in snippet view article find links to article

}}:L^{p}(\mathbb {R} ^{n})\to L^{p'}(\mathbb {R} ^{n})} is a well-defined bounded operator when 1 / p + 1 / p ′ = 1 {\displaystyle 1/p+1/p'=1} . Heaviside The