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
View via Publisher
ams.org
229 Citations
Highly Influential Citations
14
Background Citations
50
Methods Citations
16
Results Citations
1

229 Citations

Citation Type

Citation Type

Maximal Operators with Respect to the Numerical Range
Let $$\mathfrak {n}$$n be a nonempty, proper, convex subset of $$\mathbb {C}$$C. The $$\mathfrak {n}$$n-maximal operators are defined as the operators having numerical ranges in $$\mathfrak {n}$$n…
Norm preserving extensions of linear transformations on Hilbert spaces.
Introduction. Let H be a Hilbert space and let D be a closed proper subspace of H. Let Jo be a linear contraction on D to H. The problem of characterizing the contractions on all of H which extend Jo…
M-dissipative boundary conditions and boundary tuples for Maxwell operators
Dissipative extensions and port-Hamiltonian operators on networks
Extraction and prediction of coherent patterns in incompressible flows through space–time Koopman analysis
3 Boundary triplets and maximal accretive extensions of sectorial operators
This chapter is a survey of results related to the problem of a description of all maximal accretive extensions for a densely defined sectorial operator; the problem in more generality was originally…
Conditions for the maximal dissipativity of almost bounded perturbations of smooth restrictions of operators adjoint to symmetric ones
We establish conditions for the maximal dissipativity of one class of densely-defined closed linear operators in a Hilbert space. The results obtained are applied to the investigation of some special…
Differential-boundary operators and associated neutral functional differential questions
Wave operators and asymptotic solutions of wave propagation problems of classical physics
Problems in linked operators. II
...
...

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
...
...