Matches in SemOpenAlex for { <https://semopenalex.org/work/W166083085> ?p ?o ?g. }
Showing items 1 to 76 of
76
with 100 items per page.
- W166083085 abstract "To proceed further, we need the definition of the spectrum of a linear operator B taking a Banach space ℬ into itself. The resolvent set ρ(B) of B is the set of values λ in the complex plane for which the operator λI-B, I the identity operator, has a bounded inverse with domain dense in ℬ. The complement of ρ(B) in the complex plane is called the spectrum of B and is denoted by σ(B). The spectrum σ(B) of an operator may consist of three different types of points, namely the residual spectrum Rσ(B), the continuous spectrum Cσ(B) and the point spectrum Pσ(B). The residual spectrum consists of those λ in σ(B) for which (λI-B)−1 exists but D(λI-B)−1 is not dense in ℬ The continuous spectrum consists of those λ in σ(B) for which λI-B has an unbounded inverse with dense domain the point spectrum consists of those values of λ in σ(B) for which λI-B does not have an inverse. The points λ in Pσ(B) are sometimes called the eigenvalues of B and any nonzero ϕ in B such that (λI-B)ϕ = 0 is called an eigenvector. The null space ℜ(B) of B is the set of all ϕ in ℬ for which Bϕ = 0. For a given λ in σ(B) the generalized eigenspace of λ will be denoted by Mλ(B) and is defined to be the smallest subspace of ℬ containing all the elements of ℬ which belong to ℜ(λI-B)k, k = 1,2,…." @default.
- W166083085 created "2016-06-24" @default.
- W166083085 creator A5056303834 @default.
- W166083085 date "1971-01-01" @default.
- W166083085 modified "2023-09-26" @default.
- W166083085 title "The Eigenvalues of a Linear Autonomous Equation. Decomposition of C." @default.
- W166083085 doi "https://doi.org/10.1007/978-1-4615-9968-5_20" @default.
- W166083085 hasPublicationYear "1971" @default.
- W166083085 type Work @default.
- W166083085 sameAs 166083085 @default.
- W166083085 citedByCount "0" @default.
- W166083085 crossrefType "book-chapter" @default.
- W166083085 hasAuthorship W166083085A5056303834 @default.
- W166083085 hasConcept C104317684 @default.
- W166083085 hasConcept C114614502 @default.
- W166083085 hasConcept C121332964 @default.
- W166083085 hasConcept C134306372 @default.
- W166083085 hasConcept C156778621 @default.
- W166083085 hasConcept C158448853 @default.
- W166083085 hasConcept C158693339 @default.
- W166083085 hasConcept C17020691 @default.
- W166083085 hasConcept C175454919 @default.
- W166083085 hasConcept C185592680 @default.
- W166083085 hasConcept C207467116 @default.
- W166083085 hasConcept C2524010 @default.
- W166083085 hasConcept C33923547 @default.
- W166083085 hasConcept C34388435 @default.
- W166083085 hasConcept C36503486 @default.
- W166083085 hasConcept C55493867 @default.
- W166083085 hasConcept C62520636 @default.
- W166083085 hasConcept C86339819 @default.
- W166083085 hasConceptScore W166083085C104317684 @default.
- W166083085 hasConceptScore W166083085C114614502 @default.
- W166083085 hasConceptScore W166083085C121332964 @default.
- W166083085 hasConceptScore W166083085C134306372 @default.
- W166083085 hasConceptScore W166083085C156778621 @default.
- W166083085 hasConceptScore W166083085C158448853 @default.
- W166083085 hasConceptScore W166083085C158693339 @default.
- W166083085 hasConceptScore W166083085C17020691 @default.
- W166083085 hasConceptScore W166083085C175454919 @default.
- W166083085 hasConceptScore W166083085C185592680 @default.
- W166083085 hasConceptScore W166083085C207467116 @default.
- W166083085 hasConceptScore W166083085C2524010 @default.
- W166083085 hasConceptScore W166083085C33923547 @default.
- W166083085 hasConceptScore W166083085C34388435 @default.
- W166083085 hasConceptScore W166083085C36503486 @default.
- W166083085 hasConceptScore W166083085C55493867 @default.
- W166083085 hasConceptScore W166083085C62520636 @default.
- W166083085 hasConceptScore W166083085C86339819 @default.
- W166083085 hasLocation W1660830851 @default.
- W166083085 hasOpenAccess W166083085 @default.
- W166083085 hasPrimaryLocation W1660830851 @default.
- W166083085 hasRelatedWork W100983176 @default.
- W166083085 hasRelatedWork W19586112 @default.
- W166083085 hasRelatedWork W1970099212 @default.
- W166083085 hasRelatedWork W1987053818 @default.
- W166083085 hasRelatedWork W1995245627 @default.
- W166083085 hasRelatedWork W2037781894 @default.
- W166083085 hasRelatedWork W2045012088 @default.
- W166083085 hasRelatedWork W2080687987 @default.
- W166083085 hasRelatedWork W2368797503 @default.
- W166083085 hasRelatedWork W2612011191 @default.
- W166083085 hasRelatedWork W2741571301 @default.
- W166083085 hasRelatedWork W2767050690 @default.
- W166083085 hasRelatedWork W2785685360 @default.
- W166083085 hasRelatedWork W2952571638 @default.
- W166083085 hasRelatedWork W2962964957 @default.
- W166083085 hasRelatedWork W3005572443 @default.
- W166083085 hasRelatedWork W3205958452 @default.
- W166083085 hasRelatedWork W434940860 @default.
- W166083085 hasRelatedWork W3150394423 @default.
- W166083085 hasRelatedWork W92093953 @default.
- W166083085 isParatext "false" @default.
- W166083085 isRetracted "false" @default.
- W166083085 magId "166083085" @default.
- W166083085 workType "book-chapter" @default.