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FunctionSpace

Notable function spaces from functional analysis.

Entity["FunctionSpace",name] or

represents an entity of type "FunctionSpace".

[prop]

gives the value of a specified property.

[{propi,…}]

gives the value of a list of properties.

EntityClass["FunctionSpace",{propispeci,…}]

represents a class of entities with values of propi defined by speci.

Sample Entities

  • …

Sample Entity Classes

  • …

Properties

  • AdditionalPeopleadditional people involved
    AlternateNamesalternate names
    AlternateNotationsalternate notations
    AssociatedPeopleassociated people
    BesselInequalityBessel inequality
    CauchySchwarzInequalityCauchy‐Schwarz inequality
    Classesclasses
    Classificationsclassifications
    Dimensiondimension
    DualSpacedual space
    DualSpaceMapdual space map
    EmbeddingSpaceembedding space
    EntityClassesentity classes
    EntityTypeListentity type list
    EponymousPeopleeponymous people
    EquivalenceRelationequivalence relation
    FormattedASCIINameformatted ASCII name
    FormattedReferencesreferences
    FormulationDateformulation date
    Formulatorsformulators
    HoelderTypeInequalityHölder‐type inequality
    InnerProductinner product
    IsomorphicSpacesisomorphic spaces
    MeasureSpacemeasure space
    Namename
    NonorthonormalBasisExamplenonorthonormal basis example
    Normnorm
    OrthonormalBasisExampleorthonormal basis example
    ParameterRestrictionsparameter restrictions
    Parametersparameters
    PlaintextNameplaintext name
    PreDualSpacepre‐dual space
    PreDualSpaceMappre‐dual space map
    QuasiNormquasi‐norm
    Referencesreference citations
    RelatedResultsrelated results
    RelatedSpacesrelated spaces
    RelationshipGraphrelationship graph
    SampleMemberssample members
    SampleNonmemberssample nonmembers
    Seminormsseminorms
    ShortNotationshort notation
    Timelinetimeline
    TriangleInequalitytriangle inequality
    TypesetDescriptiontypeset description
    TypesetNotationsTabletypeset notations table
    UnderlyingSpaceunderlying space

Details

  • "FunctionSpace" entities include notable named function spaces parametrized based on domain and measure.
  • "FunctionSpace" entity classes include classifications based on domain and mathematical properties.
  • Some properties are available for the "FunctionSpace" entity type as a whole and can be given using the form EntityValue["FunctionSpace",property]. Such properties include:
  • "Properties"the list of available properties
    "PropertyCanonicalNames"the standard names of available properties
    "SampleEntities"a sample list of available entities (typically of length 10)
    "SampleEntityClasses"a sample list of available entity classes (typically of length 10)
    "EntityCount"number of entities available
    "Entities"the list of available entities
    "EntityCanonicalNames"the standard names of available entities
    "EntityClasses"the list of available entity classes
    "EntityClassCanonicalNames"the standard names of available entity classes
    "PropertyClasses"the list of available property classes
    "PropertyClassCanonicalNames"the standard names of available property classes
    "PropertyCount"number of properties available
  • The following annotations can be used in the third argument of EntityValue["FunctionSpace",property,annotation]:
  • "Source"source information for the property
    "Date"the date associated with the entity-property value (if any)
    "EntityAssociation"an association of entities and entity-property values
    "PropertyAssociation"an association of properties and entity-property values
    "EntityPropertyAssociation"an association in which the specified entities are keys, and values are a nested association of properties and entity-property values
    "PropertyEntityAssociation"an association in which the specified properties are keys, and values are a nested association of entities and entity-property values
    "Dataset"a dataset in which the specified entities are keys, and values are an association of property names and entity-property values
  • The following annotations can be used in the second argument of EntityValue[property,annotation]:
  • "Qualifiers"the list of possible qualifiers for the property
    "QualifierValues"the list of possible values that can be given to each qualifier
    "DefaultQualifierValues"the list of default values for the property's qualifiers
    "Description"a brief textual description of the property
    "Definition"a detailed textual definition of the property
    "PhysicalQuantity"the physical quantity associated with the entity-property value
    "Unit"the unit associated with the entity-property value
  • A qualifier value of Automatic indicates that an applicable format of values can be used; e.g. for the "Date" qualifier, this includes a proper date or date span.

Examples

Basic Examples  (4)

Use for entity discovery:

Wolfram Language code: ["lebesgue space L^2(R^n)"]

Find a property value for an entity:

Wolfram Language code: Entity["FunctionSpace", {{"LebesgueL", {{"Reals", n}, {"LebesgueMeasure", n}}}, 2}]["Norm"]

Retrieve a dataset of all available properties for an entity:

Wolfram Language code: Entity["FunctionSpace", {{"LorentzL", {{"Reals", }, {"LebesgueMeasure", }}}, {, "Infinity"}}]["Dataset"]//DeleteMissing

Retrieve tabulated function spaces that are measurable Hilbert spaces:

Wolfram Language code: EntityClass["FunctionSpace", {"Classifications" -> ContainsAll[{"HilbertSpace"}], "Classes" -> ContainsAll[{"Measurable"}]}]//EntityList