Examples of 'infinite-dimensional' in a sentence
Meaning of "infinite-dimensional"
Infinite-dimensional is an adjective used to describe a mathematical space or object that has a dimensionality that is unbounded or limitless
How to use "infinite-dimensional" in a sentence
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infinite-dimensional
Shape optimization is an infinite-dimensional optimization problem.
An infinite-dimensional domain may have discontinuous linear operators.
Fixed point theorems in infinite-dimensional spaces.
On infinite-dimensional topological groups.
There is also a generalization to infinite-dimensional spaces.
In mathematics, infinite-dimensional holomorphy is a branch of functional analysis.
Floer homology extended this to infinite-dimensional manifolds.
On every infinite-dimensional topological vector space there is a discontinuous linear map.
This argument extends to many other infinite-dimensional spaces.
The topologies on the infinite-dimensional space ℓ p are inequivalent for different p.
Such systems are therefore also known as infinite-dimensional systems.
Infinite-dimensional optimization problems can be more challenging than finite-dimensional ones.
They span up an infinite-dimensional function space.
Within it was the theme of integration of real functions in infinite-dimensional space.
Her research concerns infinite-dimensional linear systems.
See also
One distinguishes between finite-dimensional representations and infinite-dimensional ones.
Some theories possess a hidden infinite-dimensional symmetry called integrability.
Gradient descent works in spaces of any number of dimensions, even in infinite-dimensional ones.
Gaussian processes can be seen as an infinite-dimensional generalization of multivariate normal distributions.
Linear operators also play a great role in the infinite-dimensional case.
In the second part, we study some infinite-dimensional objects associated to random matrix models.
One might also generalize linear algebra to study infinite-dimensional spaces.
Infinite-dimensional vector spaces arise naturally in mathematical analysis, as function spaces, whose vectors are functions.
See spectral theorems for generalizations to infinite-dimensional vector spaces.
The precise infinite-dimensional unitary representation under which a particle transforms is part of its classification.
The symplectomorphisms from a manifold back onto itself form an infinite-dimensional pseudogroup.
The unit sphere in an infinite-dimensional Hilbert space is contractible.
The concepts of rank and determinant can not be extended to infinite-dimensional matrices.
There are many classes of infinite-dimensional Lie algebras whose representations have been studied.
A statistical model is semiparametric if it has both finite-dimensional and infinite-dimensional parameters.
It can be shown that there is no infinite-dimensional analogue of Lebesgue measure.
The most important distinction is between finite-dimensional representations and infinite-dimensional ones.
This theorem is used in infinite-dimensional Lie theory.
The superposition of different universes all coexists simultaneously in the same infinite-dimensional space.
In fact, Gaussian processes can be seen as an infinite-dimensional generalization of multivariate normal distributions.
With suitable modifications, this result can be extended to possibly unbounded operators on infinite-dimensional spaces.
This is done by specifying the infinite-dimensional Markovian structure of the rough Heston model.
The freedom of choosing a convenient basis is particularly useful in the infinite-dimensional context, see below.
It has faithful irreducible infinite-dimensional representations, such as the Weil representation described below.
It may happen that the multiplication of two representative infinite-dimensional matrices is ill-defined.
Infinite-dimensional dynamical systems, An introduction to dissipative parabolic PDEs and the theory of global attractors.
Spatio-temporal covariance functions are formulated as infinite-dimensional stochastic differential equations.
This scheme treats the case of a rather general noise term regularized in space but infinite-dimensional.
This shows that the representations of above are all infinite-dimensional irreducible unitary representations.
An infinite-dimensional exponentially convergent Luenberger-like observer is presented in order to estimate the state variables.
The concept of a holomorphic function can be extended to the infinite-dimensional spaces of functional analysis.
The infinite-dimensional generalization of the Dirichlet distribution is the Dirichletprocess.
Hilbert spaces arise naturally and frequently in mathematics and physics, typically as infinite-dimensional function spaces.
A Banach space isomorphic to all its infinite-dimensional closed subspaces is isomorphic to a separable Hilbert space.
The space of Riemannian metrics on a given differentiable manifold is an infinite-dimensional space.
