In operator theory, a dilation of an operator T on a Hilbert space H is an operator on a larger Hilbert space K, whose restriction to H composed with the...

Dilation (metric space), a function from a metric space into itself Dilation (operator theory), a dilation of an operator on a Hilbert space Dilation...

is called the center of dilation. Some congruences have fixed points and others do not. Homothety Dilation (operator theory) Montgomery, Richard (2002)...

In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete...

Stinespring's dilation theorem, also called Stinespring's factorization theorem, named after W. Forrest Stinespring, is a result from operator theory that represents...

universality. The technical term for this transformation is a dilatation (also known as dilation). Dilatations can form part of a larger conformal symmetry. In mathematics...

In operator theory, Naimark's dilation theorem is a result that characterizes positive operator valued measures. It can be viewed as a consequence of Stinespring's...

In operator theory, a bounded operator T: X → Y between normed vector spaces X and Y is said to be a contraction if its operator norm ||T || ≤ 1. This...

particular functional analysis, the shift operator, also known as the translation operator, is an operator that takes a function x ↦ f(x) to its translation...

infimum operators can be replaced by the maximum and minimum. Thus, dilation and erosion are particular cases of order statistics filters, with dilation returning...

In a scale invariant quantum field theory, by definition each operator O {\displaystyle O} acquires under a dilation x → λ x {\displaystyle x\to \lambda...

Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this...

O_{1}(x_{1})O_{2}(x_{2})\right\rangle =0.} If the dilation operator is diagonalizable (i.e. if the theory is not logarithmic), there exists a basis of primary...

which represents the quantum-mechanical breaking of scale (dilation) symmetry in a field theory. Applications of the RG to particle physics exploded in number...

In operator theory, a branch of mathematics, a positive-definite kernel is a generalization of a positive-definite function or a positive-definite matrix...

representation theorem are described in Classical function theory, Operator Dilation Theory, and Machine Computations on Multiply-Connected Domains. "List...

fields' distance. Equivalently, the dilation operator is not diagonalizable. Examples of logarithmic conformal field theories include critical percolation....

Hamiltonian, a positive-definite operator which annihilates the vacuum. A construction of a quantum scalar field theory is detailed in the canonical quantization...

gravitational time dilation. Gravitational redshift has been measured in the laboratory and using astronomical observations. Gravitational time dilation in the Earth's...

(Δx) in its own rest frame (S). Time dilation and length contraction are not merely appearances. Time dilation is explicitly related to our way of measuring...

Complement of a point, the dilation of a point in the centroid of a given triangle, with ratio −1/2 Complement (set theory) Complementary event in probability...

In quantum information theory and operator theory, the Choi–Jamiołkowski isomorphism refers to the correspondence between quantum channels (described by...

to the effects of length contraction and time dilation, both predicted results of Albert Einstein's theory of general relativity. Because of the bending...

especially operator theory, subnormal operators are bounded operators on a Hilbert space defined by weakening the requirements for normal operators. Some examples...

representation of C*-algebras by bounded operators Naimark's dilation theorem on extensions of symmetric operators The Gelfand–Naimark–Segal construction...

min-max theory, Bahri and Lions were able to establish multiplicity results for these problems.[BL88] Lions also considered the problem of dilation invariance...

synchronization). By giving the effects of time dilation and length contraction the exact relativistic value, this test theory is experimentally equivalent to special...

information science, a positive operator-valued measure (POVM) is a measure whose values are positive semi-definite operators on a Hilbert space. POVMs are...

numbers or other field. The differential operator X d d X {\displaystyle X{\frac {d}{dX}}} is invariant under dilation (replacing X by aX for a constant)....

unitary groups (functional analysis) Sz.-Nagy's dilation theorem (operator theory) Tomita's theorem (operator algebras) Von Neumann bicommutant theorem (functional...