DISSIPATIVE OPERATORS AND HYPERBOLIC SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS

@article{Phillips1959DISSIPATIVEOA,
  title={DISSIPATIVE OPERATORS AND HYPERBOLIC SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS},
  author={Ralph Phillips},
  journal={Transactions of the American Mathematical Society},
  year={1959},
  volume={90},
  pages={193-254}
}
  • R. Phillips
  • Published 1 February 1959
  • Mathematics
  • Transactions of the American Mathematical Society
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234 Citations
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15
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234 Citations

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References

SHOWING 1-10 OF 20 REFERENCES
Functional Analysis and Semi-Groups
THIS work of Prof. Einar Hille is one of the important mathematical books of the century ; it should be read seriously by every mathematician. The subject of semi-groups is one of great and growing…
Dissipative hyperbolic systems
One-Parameter Semigroups of Isometric Operators in Hilbert Space
The theory of one-parameter groups of unitary operators in Hilbert Space due to Stone' shows that to such a group there corresponds a selfadjoint operator which is the infinitesimal operator of the…
THE PARABOLIC DIFFERENTIAL EQUATIONS AND THE ASSOCIATED SEMI-GROUPS OF TRANSFORMATIONS
On the theory of general partial differential operators
I I . Min ima l d i f fe ren t i a l ope ra to r s w i t h c o n s t a n t coeff ic ients . I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 N o t a t i o n s…
Symmetric Operators in Hilbert Space
An operator-theoretical integration of the wave equation.
Abstract symmetric boundary conditions
MEASURE AND AREA
Abstract : The original program is described for a project which called for providing adequate foundations in measure theory for application to certain fundamental problems in the theor of surface…
LivSic, On the spectral decomposition of linear nons elf-adjoint operators, Mat
  • Sbornik, N. S. vol
  • 1954
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