Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Spectrum_(functional_analysis)> ?p ?o. }
Showing items 1 to 32 of
32
with 100 items per page.
- Spectrum_(functional_analysis) abstract "In functional analysis, the concept of the spectrum of a bounded operator is a generalisation of the concept of eigenvalues for matrices. Specifically, a complex number λ is said to be in the spectrum of a bounded linear operator T if λI − T is not invertible, where I is the identity operator. The study of spectra and related properties is known as spectral theory, which has numerous applications, most notably the mathematical formulation of quantum mechanics.The spectrum of an operator on a finite-dimensional vector space is precisely the set of eigenvalues. However an operator on an infinite-dimensional space may have additional elements in its spectrum, and may have no eigenvalues. For example, consider the right shift operator R on the Hilbert space ℓ2,This has no eigenvalues, since if Rx=λx then by expanding this expression we see that x1=0, x2=0, etc. On the other hand 0 is in the spectrum because the operator R − 0 (i.e. R itself) is not invertible: it is not surjective since any vector with non-zero first component is not in its range. In fact every bounded linear operator on a complex Banach space must have a non-empty spectrum.The notion of spectrum extends to densely defined unbounded operators. In this case a complex number λ is said to be in the spectrum of such an operator T:D→X (where D is dense in X) if there is no bounded inverse (λI − T)−1:X→D. If T is a closed operator (which includes the case that T is a bounded operator), boundedness of such inverses follow automatically if the inverse exists at all.The space of bounded linear operators B(X) on a Banach space X is an example of a unital Banach algebra. Since the definition of the spectrum does not mention any properties of B(X) except those that any such algebra has, the notion of a spectrum may be generalised to this context by using the same definition verbatim.".
- Spectrum_(functional_analysis) wikiPageID "206137".
- Spectrum_(functional_analysis) wikiPageRevisionID "604773087".
- Spectrum_(functional_analysis) hasPhotoCollection Spectrum_(functional_analysis).
- Spectrum_(functional_analysis) id "p/s086610".
- Spectrum_(functional_analysis) title "Spectrum of an operator".
- Spectrum_(functional_analysis) subject Category:Spectral_theory.
- Spectrum_(functional_analysis) comment "In functional analysis, the concept of the spectrum of a bounded operator is a generalisation of the concept of eigenvalues for matrices. Specifically, a complex number λ is said to be in the spectrum of a bounded linear operator T if λI − T is not invertible, where I is the identity operator.".
- Spectrum_(functional_analysis) label "Espectro (matemática)".
- Spectrum_(functional_analysis) label "Espectro de un operador".
- Spectrum_(functional_analysis) label "Spectre d'un opérateur linéaire".
- Spectrum_(functional_analysis) label "Spectrum (functionaalanalyse)".
- Spectrum_(functional_analysis) label "Spectrum (functional analysis)".
- Spectrum_(functional_analysis) label "Spektrum (Operatortheorie)".
- Spectrum_(functional_analysis) label "Spettro (matematica)".
- Spectrum_(functional_analysis) label "Widmo (matematyka)".
- Spectrum_(functional_analysis) label "Спектр оператора".
- Spectrum_(functional_analysis) label "スペクトル (関数解析学)".
- Spectrum_(functional_analysis) sameAs Spektrum_(Operatortheorie).
- Spectrum_(functional_analysis) sameAs Espectro_de_un_operador.
- Spectrum_(functional_analysis) sameAs Spectre_d'un_opérateur_linéaire.
- Spectrum_(functional_analysis) sameAs Spettro_(matematica).
- Spectrum_(functional_analysis) sameAs スペクトル_(関数解析学).
- Spectrum_(functional_analysis) sameAs 스펙트럼_(함수해석학).
- Spectrum_(functional_analysis) sameAs Spectrum_(functionaalanalyse).
- Spectrum_(functional_analysis) sameAs Widmo_(matematyka).
- Spectrum_(functional_analysis) sameAs Espectro_(matemática).
- Spectrum_(functional_analysis) sameAs m.01d77l.
- Spectrum_(functional_analysis) sameAs Q1365748.
- Spectrum_(functional_analysis) sameAs Q1365748.
- Spectrum_(functional_analysis) wasDerivedFrom Spectrum_(functional_analysis)?oldid=604773087.
- Spectrum_(functional_analysis) isPrimaryTopicOf Spectrum_(functional_analysis).