Faster access than browser!Similarities between Fredholm operator and Hilbert space
Fredholm operator and Hilbert space have 14 things in common (in Unionpedia): Atiyah–Singer index theorem, Banach space, Bounded operator, Cokernel, Compact operator, Dimension, Hardy space, Hermitian adjoint, Integral equation, Kernel (algebra), Kernel (linear algebra), Mathematics, Operator norm, Partial differential equation.
Atiyah–Singer index theorem
In differential geometry, the Atiyah–Singer index theorem, proved by, states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data).
Atiyah–Singer index theorem and Fredholm operator · Atiyah–Singer index theorem and Hilbert space ·
Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
Banach space and Fredholm operator · Banach space and Hilbert space ·
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).
Bounded operator and Fredholm operator · Bounded operator and Hilbert space ·
Cokernel
In mathematics, the cokernel of a linear mapping of vector spaces f: X → Y is the quotient space Y/im(f) of the codomain of f by the image of f. The dimension of the cokernel is called the corank of f. Cokernels are dual to the kernels of category theory, hence the name: the kernel is a subobject of the domain (it maps to the domain), while the cokernel is a quotient object of the codomain (it maps from the codomain).
Cokernel and Fredholm operator · Cokernel and Hilbert space ·
Compact operator
In functional analysis, a branch of mathematics, a compact operator is a linear operator L from a Banach space X to another Banach space Y, such that the image under L of any bounded subset of X is a relatively compact subset (has compact closure) of Y. Such an operator is necessarily a bounded operator, and so continuous.
Compact operator and Fredholm operator · Compact operator and Hilbert space ·
Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
Dimension and Fredholm operator · Dimension and Hilbert space ·
Hardy space
In complex analysis, the Hardy spaces (or Hardy classes) Hp are certain spaces of holomorphic functions on the unit disk or upper half plane.
Fredholm operator and Hardy space · Hardy space and Hilbert space ·
Hermitian adjoint
In mathematics, specifically in functional analysis, each bounded linear operator on a complex Hilbert space has a corresponding adjoint operator.
Fredholm operator and Hermitian adjoint · Hermitian adjoint and Hilbert space ·
Integral equation
In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign.
Fredholm operator and Integral equation · Hilbert space and Integral equation ·
Kernel (algebra)
In the various branches of mathematics that fall under the heading of abstract algebra, the kernel of a homomorphism measures the degree to which the homomorphism fails to be injective.
Fredholm operator and Kernel (algebra) · Hilbert space and Kernel (algebra) ·
Kernel (linear algebra)
In mathematics, and more specifically in linear algebra and functional analysis, the kernel (also known as null space or nullspace) of a linear map between two vector spaces V and W, is the set of all elements v of V for which, where 0 denotes the zero vector in W. That is, in set-builder notation,.
Fredholm operator and Kernel (linear algebra) · Hilbert space and Kernel (linear algebra) ·
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
Fredholm operator and Mathematics · Hilbert space and Mathematics ·
Operator norm
In mathematics, the operator norm is a means to measure the "size" of certain linear operators.
Fredholm operator and Operator norm · Hilbert space and Operator norm ·
Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
Fredholm operator and Partial differential equation · Hilbert space and Partial differential equation ·
The list above answers the following questions
- What Fredholm operator and Hilbert space have in common
- What are the similarities between Fredholm operator and Hilbert space
Fredholm operator and Hilbert space Comparison
Fredholm operator has 27 relations, while Hilbert space has 298. As they have in common 14, the Jaccard index is 4.31% = 14 / (27 + 298).
References
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