caa a22 4500 467931674 CHVBK 20180406152945.0 cr unu---uuuuu 170328e20060601xx s 000 0 eng 10.1007/s00020-005-1385-1 doi (NATIONALLICENCE)springer-10.1007/s00020-005-1385-1 An Inverse Spectral Problem for a Nonsymmetric Differential Operator: Uniqueness and Reconstruction Formula [Elektronische Daten] [Wuqing Ning, Masahiro Yamamoto] Abstract.: We consider an eigenvalue problem for a system on [0, 1]: $$\left\{ {\begin{array}{*{20}l} {\left[ {\left( {\begin{array}{*{20}c} 0 & 1 \\ 1 & 0 \\ \end{array} } \right)\frac{{\text{d}}} {{{\text{d}}x}} + \left( {\begin{array}{*{20}c} {p_{11} (x)} & {p_{12} (x)} \\ {p_{21} (x)} & {p_{22} (x)} \\ \end{array} } \right)} \right]\left( {\begin{array}{*{20}c} {\varphi ^{(1)} (x)} \\ {\varphi ^{(2)} (x)} \\ \end{array} } \right) = \lambda \left( {\begin{array}{*{20}c} {\varphi ^{(1)} (x)} \\ {\varphi ^{(1)} (x)} \\ \end{array} } \right)} \\ {\varphi ^{(2)} (0)\cosh \mu - \varphi ^{(1)} (0)\sinh \mu = \varphi ^{(2)} (1)\cosh \nu + \varphi ^{(1)} (1)\sinh \nu = 0} \\ \end{array} } \right.$$ with constants $$\mu ,\nu \in \mathbb{C}.$$ Under the assumption that p21, p22 are known, we prove a uniqueness theorem and provide a reconstruction formula for p11 and p12 from the spectral characteristics consisting of one spectrum and the associated norming constants. Birkhäuser Verlag, Basel, 2006 Inverse spectral problem nationallicence nonsymmetric differential operator nationallicence Ning Wuqing Department of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro, 153, Tokyo, Japan aut Yamamoto Masahiro Department of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro, 153, Tokyo, Japan aut Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 55/2(2006-06-01), 273-304 0378-620X 55:2<273 2006 55 20 https://doi.org/10.1007/s00020-005-1385-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-005-1385-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ning Wuqing Department of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro, 153, Tokyo, Japan aut NATIONALLICENCE 700 1- Yamamoto Masahiro Department of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro, 153, Tokyo, Japan aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 55/2(2006-06-01), 273-304 0378-620X 55:2<273 2006 55 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer