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Dissipative operators and hyperbolic systems of partial differential equations
Author:
R. S. Phillips
Journal:
Trans. Amer. Math. Soc. 90 (1959), 193-254
MSC:
Primary 35.00; Secondary 46.00
MathSciNet review:
0104919
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
- [1]
J.
W. Calkin, Abstract symmetric boundary
conditions, Trans. Amer. Math. Soc.
45 (1939), no. 3,
369–442. MR
1501997, http://dx.doi.org/10.1090/S0002-9947-1939-1501997-7
- [2]
J.
L. B. Cooper, One-parameter semigroups of isometric operators in
Hilbert space, Ann. of Math. (2) 48 (1947),
827–842. MR 0027129
(10,257a)
- [3]
J.
L. B. Cooper, Symmetric operators in Hilbert space, Proc.
London Math. Soc. (2) 50 (1948), 11–55. MR 0024058
(9,446b)
- [4]
Herbert
Federer, Measure and area, Bull. Amer. Math. Soc. 58 (1952), 306–378. MR 0049289
(14,149e), http://dx.doi.org/10.1090/S0002-9904-1952-09586-0
- [5]
William
Feller, The parabolic differential equations and the associated
semi-groups of transformations, Ann. of Math. (2) 55
(1952), 468–519. MR 0047886
(13,948a)
- [6]
K.
O. Friedrichs, Symmetric hyperbolic linear differential
equations, Comm. Pure Appl. Math. 7 (1954),
345–392. MR 0062932
(16,44c)
- [7]
Einar
Hille and Ralph
S. Phillips, Functional analysis and semi-groups, American
Mathematical Society Colloquium Publications, vol. 31, American
Mathematical Society, Providence, R. I., 1957. rev. ed. MR 0089373
(19,664d)
- [8]
Lars
Hörmander, On the theory of general partial differential
operators, Acta Math. 94 (1955), 161–248. MR 0076151
(17,853d)
- [9]
M.
S. Livšic, On spectral decomposition of linear
nonself-adjoint operators, Mat. Sbornik N.S. 34(76)
(1954), 145–199 (Russian). MR 0062955
(16,48f)
- [10]
B.
R. Mukminov, On expansion with respect to the eigenfunctions of
dissipative kernels, Dokl. Akad. Nauk SSSR (N.S.) 99
(1954), 499–502 (Russian). MR 0068106
(16,830d)
- [11]
B. de Sz. Nagy, Spektraldarstellung linearer Transformationen des Hilbertschen Raumes, Ergebnisse d. Math. vol. 5 (1942).
- [12]
R.
S. Phillips, Dissipative hyperbolic
systems, Trans. Amer. Math. Soc. 86 (1957), 109–173. MR 0090748
(19,863d), http://dx.doi.org/10.1090/S0002-9947-1957-0090748-2
- [13]
M.
I. Višik, On general boundary problems for elliptic
differential equations, Trudy Moskov. Mat. Obšč.
1 (1952), 187–246 (Russian). MR 0051404
(14,473d)
- [14]
Kôsaku
Yosida, An operator-theoretical integration of the wave
equation, J. Math. Soc. Japan 8 (1956), 79–92.
MR
0107085 (21 #5812)
- [1]
- J. W. Calkin, Abstract symmetric boundary conditions, Trans. Amer. Math. Soc. vol. 45 (1939) pp. 369-442. MR 1501997
- [2]
- J. L. B. Cooper, One parameter semi-groups of isometric operators in Hilbert space, Ann. of Math. vol. 48 (2) (1947) pp. 827-842. MR 0027129 (10:257a)
- [3]
- -, Symmetric operators in Hilbert space, Proc. London Math. Soc. vol. 50 (2) (1948) pp. 11-15. MR 0024058 (9:446b)
- [4]
- H. Federer, Measure and area, Bull. Amer. Math. Soc. vol. 58 (1952) pp. 306-378. MR 0049289 (14:149e)
- [5]
- W. Feller, The parabolic differential equations and the associated semi-groups of transformations, Ann. of Math. vol. 55 (1952) pp. 468-519. MR 0047886 (13:948a)
- [6]
- K. O. Friedrichs, Symmetric hyperbolic linear differential equations, Comm. Pure Appl. Math. vol. 7 (1954) pp. 345-392. MR 0062932 (16:44c)
- [7]
- E. Hille and R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc. Colloquium Publications, vol. 31, 1957. MR 0089373 (19:664d)
- [8]
- Lars Hörmander, General partial differential operators, Acta Math. vol. 94 (1955) pp. 161-248. MR 0076151 (17:853d)
- [9]
- M. S. Livšlc, On the spectral decomposition of linear nonself-adjoint operators, Mat. Sbornik, N. S. vol. 34 (76) (1954) pp. 145-199. MR 0062955 (16:48f)
- [10]
- B. R. Mukminov, On expansions with respect to the eigenfunctions of dissipative kernels, Doklady Akad. Nauk. SSSR, N. S. vol. 99 (1954) pp. 499-502. MR 0068106 (16:830d)
- [11]
- B. de Sz. Nagy, Spektraldarstellung linearer Transformationen des Hilbertschen Raumes, Ergebnisse d. Math. vol. 5 (1942).
- [12]
- R. S. Phillips, Dissipative hyperbolic systems, Trans. Amer. Math. Soc. vol. 86 (1957) pp. 109-173. MR 0090748 (19:863d)
- [13]
- M. I. Višik, On general boundary problems for elliptic differential equations, Trudy Moskov. Mat. Obšč. vol. 1 (1952) pp. 187-246. MR 0051404 (14:473d)
- [14]
- Kôsaku Yosida, An operator-theoretical integration of the wave equation, J. Math. Soc. Japan vol. 8 (1956) pp. 79-92. MR 0107085 (21:5812)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1959-0104919-1
PII:
S 0002-9947(1959)0104919-1
Article copyright:
© Copyright 1959 American Mathematical Society
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