FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1754577265> ?p ?o ?g. }

• W1754577265 endingPage "3262" @default.
• W1754577265 startingPage "3229" @default.
• W1754577265 abstract "This paper is a sequel to a paper by the second author on regular linear systems (1994), referred to here as “Part I”. We introduce the system operator of a well-posed linear system, which for a finite-dimensional system described by $dot x=Ax+Bu$, $y=Cx+Du$ would be the $s$-dependent matrix $S_Sigma (s)= left [ {}^{A-sI}_{ ; C} { } ^{B}_{D} right ]$. In the general case, $S_Sigma (s)$ is an unbounded operator, and we show that it can be split into four blocks, as in the finite-dimensional case, but the splitting is not unique (the upper row consists of the uniquely determined blocks $A-sI$ and $B$, as in the finite-dimensional case, but the lower row is more problematic). For weakly regular systems (which are introduced and studied here), there exists a special splitting of $S_Sigma (s)$ where the right lower block is the feedthrough operator of the system. Using $S_Sigma (0)$, we give representation theorems which generalize those from Part I to well-posed linear systems and also to the situation when the “initial time” is $-infty$. We also introduce the Lax-Phillips semigroup $boldsymbol {mathfrak {T}}$ induced by a well-posed linear system, which is in fact an alternative representation of a system, used in scattering theory. Our concept of a Lax-Phillips semigroup differs in several respects from the classical one, for example, by allowing an index ${omega }in {mathbb R}$ which determines an exponential weight in the input and output spaces. This index allows us to characterize the spectrum of $A$ and also the points where $S_Sigma (s)$ is not invertible, in terms of the spectrum of the generator of $boldsymbol {mathfrak {T}}$ (for various values of ${omega }$). The system $Sigma$ is dissipative if and only if $boldsymbol {mathfrak {T}}$ (with index zero) is a contraction semigroup." @default.
• W1754577265 created "2016-06-24" @default.
• W1754577265 creator A5009609680 @default.
• W1754577265 creator A5062257326 @default.
• W1754577265 date "2002-04-03" @default.
• W1754577265 modified "2023-10-17" @default.
• W1754577265 title "Transfer functions of regular linear systems Part II: The system operator and the Lax–Phillips semigroup" @default.
• W1754577265 cites W132239807 @default.
• W1754577265 cites W1492498476 @default.
• W1754577265 cites W1527296550 @default.
• W1754577265 cites W1868559974 @default.
• W1754577265 cites W1929958170 @default.
• W1754577265 cites W1945843680 @default.
• W1754577265 cites W1974962318 @default.
• W1754577265 cites W1984694267 @default.
• W1754577265 cites W1985201527 @default.
• W1754577265 cites W1986653700 @default.
• W1754577265 cites W1991059830 @default.
• W1754577265 cites W1992378900 @default.
• W1754577265 cites W1992913239 @default.
• W1754577265 cites W1997113731 @default.
• W1754577265 cites W1997566111 @default.
• W1754577265 cites W2002475330 @default.
• W1754577265 cites W2016038884 @default.
• W1754577265 cites W2017484113 @default.
• W1754577265 cites W2027256132 @default.
• W1754577265 cites W2029710005 @default.
• W1754577265 cites W2030958501 @default.
• W1754577265 cites W2033287512 @default.
• W1754577265 cites W2037672885 @default.
• W1754577265 cites W2039646446 @default.
• W1754577265 cites W2042197953 @default.
• W1754577265 cites W2049892514 @default.
• W1754577265 cites W2053449213 @default.
• W1754577265 cites W2066605554 @default.
• W1754577265 cites W2066683359 @default.
• W1754577265 cites W2068560252 @default.
• W1754577265 cites W2073944311 @default.
• W1754577265 cites W2080056193 @default.
• W1754577265 cites W2086977179 @default.
• W1754577265 cites W2095186356 @default.
• W1754577265 cites W2097071461 @default.
• W1754577265 cites W2101758870 @default.
• W1754577265 cites W2117470445 @default.
• W1754577265 cites W2121096159 @default.
• W1754577265 cites W2133627030 @default.
• W1754577265 cites W2134372275 @default.
• W1754577265 cites W2156127866 @default.
• W1754577265 cites W2165368325 @default.
• W1754577265 cites W2170358486 @default.
• W1754577265 cites W2173130135 @default.
• W1754577265 cites W2178158283 @default.
• W1754577265 cites W2737174450 @default.
• W1754577265 cites W3038830718 @default.
• W1754577265 cites W579204254 @default.
• W1754577265 cites W139048544 @default.
• W1754577265 doi "https://doi.org/10.1090/s0002-9947-02-02976-8" @default.
• W1754577265 hasPublicationYear "2002" @default.
• W1754577265 type Work @default.
• W1754577265 sameAs 1754577265 @default.
• W1754577265 citedByCount "96" @default.
• W1754577265 countsByYear W17545772652012 @default.
• W1754577265 countsByYear W17545772652013 @default.
• W1754577265 countsByYear W17545772652014 @default.
• W1754577265 countsByYear W17545772652015 @default.
• W1754577265 countsByYear W17545772652016 @default.
• W1754577265 countsByYear W17545772652017 @default.
• W1754577265 countsByYear W17545772652018 @default.
• W1754577265 countsByYear W17545772652019 @default.
• W1754577265 countsByYear W17545772652020 @default.
• W1754577265 countsByYear W17545772652021 @default.
• W1754577265 countsByYear W17545772652022 @default.
• W1754577265 countsByYear W17545772652023 @default.
• W1754577265 crossrefType "journal-article" @default.
• W1754577265 hasAuthorship W1754577265A5009609680 @default.
• W1754577265 hasAuthorship W1754577265A5062257326 @default.
• W1754577265 hasBestOaLocation W17545772651 @default.
• W1754577265 hasConcept C104317684 @default.
• W1754577265 hasConcept C114614502 @default.
• W1754577265 hasConcept C118615104 @default.
• W1754577265 hasConcept C121332964 @default.
• W1754577265 hasConcept C134306372 @default.
• W1754577265 hasConcept C158448853 @default.
• W1754577265 hasConcept C17020691 @default.
• W1754577265 hasConcept C172829509 @default.
• W1754577265 hasConcept C185592680 @default.
• W1754577265 hasConcept C200741047 @default.
• W1754577265 hasConcept C202444582 @default.
• W1754577265 hasConcept C207405024 @default.
• W1754577265 hasConcept C2778049214 @default.
• W1754577265 hasConcept C33923547 @default.
• W1754577265 hasConcept C49766605 @default.
• W1754577265 hasConcept C55493867 @default.
• W1754577265 hasConcept C62520636 @default.
• W1754577265 hasConcept C6802819 @default.
• W1754577265 hasConcept C86339819 @default.
• W1754577265 hasConceptScore W1754577265C104317684 @default.
• W1754577265 hasConceptScore W1754577265C114614502 @default.

• next