Algebraic-differential transformations of linear differential operators of arbitrary order and their spectral properties applicable to the inverse problem. I. The case of finite $\mathfrak N$
Sbornik. Mathematics, Tome 16 (1972) no. 3, pp. 408-428
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Linear differential operators $R$ of order $n$ from $C^n[0,1]$ into $C[0,1]$, i.e. without boundary conditions, are discussed. With $\lambda$ complex, let $Z^R_\lambda$ denote the linear space of all solutions $z(x)\in C^n[0,1]$ of the homogeneous equation $Rz=\lambda z$. We use die operator $R$ and certain of its spectral properties to obtain an operator $L$ analogous to $R$. Our main result is to obtain expressions defining a linear mapping $T_\lambda\colon Z_\lambda^R\to Z_\lambda^L$ (Theorem 2.6). The linear mappings $T_\lambda$ are meromorphically dependent on $\lambda$. Bibliography: 2 titles.
@article{SM_1972_16_3_a6,
author = {Z. I. Leibenzon},
title = {Algebraic-differential transformations of linear differential operators of arbitrary order and their spectral properties applicable to the inverse problem. {I.~The} case of finite~$\mathfrak N$},
journal = {Sbornik. Mathematics},
pages = {408--428},
year = {1972},
volume = {16},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1972_16_3_a6/}
}
TY - JOUR AU - Z. I. Leibenzon TI - Algebraic-differential transformations of linear differential operators of arbitrary order and their spectral properties applicable to the inverse problem. I. The case of finite $\mathfrak N$ JO - Sbornik. Mathematics PY - 1972 SP - 408 EP - 428 VL - 16 IS - 3 UR - http://geodesic.mathdoc.fr/item/SM_1972_16_3_a6/ LA - en ID - SM_1972_16_3_a6 ER -
%0 Journal Article %A Z. I. Leibenzon %T Algebraic-differential transformations of linear differential operators of arbitrary order and their spectral properties applicable to the inverse problem. I. The case of finite $\mathfrak N$ %J Sbornik. Mathematics %D 1972 %P 408-428 %V 16 %N 3 %U http://geodesic.mathdoc.fr/item/SM_1972_16_3_a6/ %G en %F SM_1972_16_3_a6
Z. I. Leibenzon. Algebraic-differential transformations of linear differential operators of arbitrary order and their spectral properties applicable to the inverse problem. I. The case of finite $\mathfrak N$. Sbornik. Mathematics, Tome 16 (1972) no. 3, pp. 408-428. http://geodesic.mathdoc.fr/item/SM_1972_16_3_a6/
[1] Z. L. Leibenzon, “Obratnaya zadacha spektralnogo analiza obyknovennykh differentsialnykh operatorov vysshikh poryadkov”, Trudy Mosk. matem. ob-va, XV (1966), 70–144 | MR
[2] Z. L. Leibenzon, “Edinstvennost resheniya obratnoi zadachi dlya obyknovennykh differentsialnykh operatorov poryadka $n\geqslant2$ i preobrazovaniya takikh operatorov”, DAN SSSR, 142:3 (1962), 534–537 | MR | Zbl