Geodesic
On functions of a positive operator
Sbornik. Mathematics, Tome 47 (1984) no. 1, pp. 27-42 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For functions $\varphi(1/z)=b+\int_0^\infty(z+s)^{-1}d\sigma(s)$, $b>0$, $\sigma(s)$ nondecreasing, and $A$ a positive operator in a Banach space, the operators $\varphi(A^{-1})$ and $\varphi(A)$ are constructed, their products and superpositions are investigated and the moment inequality as well as other estimates are proved. The results are generalized to the case when $A^{-1}$ does not exist or is not bounded. Bibliography: 21 titles. 
@article{SM_1984_47_1_a1,
     author = {E. I. Pustyl'nik},
     title = {On~functions of a positive operator},
     journal = {Sbornik. Mathematics},
     pages = {27--42},
     year = {1984},
     volume = {47},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_47_1_a1/}
}
TY  - JOUR
AU  - E. I. Pustyl'nik
TI  - On functions of a positive operator
JO  - Sbornik. Mathematics
PY  - 1984
SP  - 27
EP  - 42
VL  - 47
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1984_47_1_a1/
LA  - en
ID  - SM_1984_47_1_a1
ER  - 
%0 Journal Article
%A E. I. Pustyl'nik
%T On functions of a positive operator
%J Sbornik. Mathematics
%D 1984
%P 27-42
%V 47
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1984_47_1_a1/
%G en
%F SM_1984_47_1_a1
E. I. Pustyl'nik. On functions of a positive operator. Sbornik. Mathematics, Tome 47 (1984) no. 1, pp. 27-42. http://geodesic.mathdoc.fr/item/SM_1984_47_1_a1/

[1] Krasnoselskii M. A., Sobolevskii P. E., “Drobnye stepeni operatorov, deistvuyuschikh v banakhovykh prostranstvakh”, DAN SSSR, 129:3 (1959), 499–502 | MR

[2] Agmon S., Duglis A., Nirenberg L., Otsenki reshenii ellipticheskikh uravnenii vblizi granitsy, IL, M., 1962

[3] Krein S. G., Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967 | MR

[4] Sobolevskii P. E., “O logarifmakh normalno pozitivnykh operatorov”, UMN, 16:4 (1961), 206–208

[5] Nollau V., “Über den logarithmus abgeschloßener Operatoren in Banachschen Räumen”, Acta Sci. Math., 30 (1969), 161–174 | MR | Zbl

[6] Yoshikawa A., “On the logarithm of closed linear operators”, Proc. Japan Acad., 49:3 (1973), 169–173 | DOI | MR | Zbl

[7] Sobolevskii P. E., Yasakov A. I., “Ob uravneniyakh parabolicheskogo tipa s nestepennymi nelineinostyami”, Diff. uravneniya, 7:8 (1971), 1503–1511 | MR | Zbl

[8] Pustylnik E. I., “O nekotorykh svoistvakh vognutykh funktsii samosopryazhennogo operatora”, DAN SSSR, 186:6 (1969), 1259–1261 | MR

[9] Pustylnik E. I., “Interpolyatsionnye teoremy v massivakh banakhovykh prostranstv”, DAN SSSR, 224:5 (1975), 1024–1027 | MR

[10] Pustylnik E. I., Kvazivognutye funktsii, Dep. VINITI, No 1202-79, 1979 | MR

[11] Akhiezer N. I., Klassicheskaya problema momentov, Fizmatgiz, M., 1961

[12] Hirsch F., “Intégrales de résolvantes et calcul symbolique”, Ann. Inst. Fourier, 22:4 (1972), 239–264 | MR | Zbl

[13] Pustylnik E. I., “Absolyutno vognutye funktsii pozitivnykh operatorov”, DAN SSSR, 228:3 (1976), 547–550 | MR

[14] Khirshman I. I., Uidder D. V., Preobrazovaniya tipa svertki, IL, M., 1958

[15] Pustylnik E. I., “O sootnosheniyakh podchinennosti dlya vognutykh funktsii samosopryazhennykh operatorov”, DAN SSSR, 224:6 (1975), 1264–1267 | MR

[16] Krein S. G., Petunin Yu. I., Semenov E. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978 | MR

[17] Tribel X., Teoriya interpolyatsii, funktsionalnye prostranstva, differentsialnye operatory, Mir, M., 1980 | MR

[18] Peetre J., “A theory of interpolation of normed spaces”, Notes Universidad de Brazilia, 1963

[19] Dmitriev A. A., “Ob interpolyatsii odnomernykh operatorov”, Trudy NII matem. Voronezhskogo un-ta, 1973, no. 11, 31–43 | MR

[20] Pustylnik E. I., “O maksimalnykh i minimalnykh promezhutochnykh prostranstvakh”, Ukr. matem. zh., 29:1 (1977), 129–137 | MR