1.

Record Nr.

UNINA9910154743403321

Autore

Boutet de Monvel L.

Titolo

The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 / / L. Boutet de Monvel, Victor Guillemin

Pubbl/distr/stampa

Princeton, NJ : , : Princeton University Press, , [2016]

©1981

ISBN

1-4008-8144-7

Descrizione fisica

1 online resource (168 pages)

Collana

Annals of Mathematics Studies ; ; 240

Disciplina

515.7/246

Soggetti

Toeplitz operators

Spectral theory (Mathematics)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

Frontmatter -- TABLE OF CONTENTS -- §1. Introduction -- §2. GENERALIZED TOEPLITZ OPERATORS -- §3. FOURIER INTEGRAL OPERATORS OF HERMITE TYPE -- §4. THE METAPLECTIC REPRESENTATION -- §5. METALINEAR AND METAPLECTIC STRUCTURES ON MANIFOLDS -- §6. ISOTROPIC SUBSPACES OF SYMPLECTIC VECTOR SPACES -- §7. THE COMPOSITION THEOREM -- §8. THE PROOF OF THEOREM 7.5 -- §9. PULL-BACKS, PUSH-FORWARDS AND EXTERIOR TENSOR PRODUCTS -- §10. THE TRANSPORT EQUATION -- §11. SYMBOLIC PROPERTIES OF TOEPLITZ OPERATORS -- §12. THE TRACE FORMULA -- §13. SPECTRAL PROPERTIES OF TOEPLITZ OPERATORS -- §14. THE HILBERT POLYNOMIAL -- §15. SOME CONCLUDING REMARKS -- BIBLIOGRAPHY -- APPENDIX: QUANTIZED CONTACT STRUCTURES -- Backmatter

Sommario/riassunto

The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations.If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete



spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol.It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the "quantized" objects associated with functions on compact contact manifolds.

2.

Record Nr.

UNINA9910817827003321

Titolo

Cassius Dio : the impact of violence, war, and civil war / / edited by Carsten H. Lange, Andrew G. Scott

Pubbl/distr/stampa

Leiden ; ; Boston : , : Brill, , [2020]

©2020

ISBN

90-04-43443-7

Descrizione fisica

1 online resource

Collana

Historiography of Rome and its empire ; ; Volume 8

Disciplina

937.0072

Soggetti

Civil war - Rome - Historiography

Rome Republic, 265-30 B.C Historiography

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Includes index.

Nota di contenuto

Violence as an Interpretive Category in Cassius Dio: the Terror under Sulla in 82 BCE / Piotr Berdowski -- Gossip of Violence and Violence of Gossip: Livia's Lament and Its Remedy in Cassius Dio's Severan Context / Joel Allen -- Causation and Morality: Cassius Dio on the Origins of Rome's External Wars under the Republic / John Rich -- Caesar's Campaigns in Cassius Dio's Late Republic / Mads Ortving Lindholmer -- Cassius Dio and the Roman Empire: the Impact of the Severan Wars on Dio's Narrative / Estelle Bertrand -- "A Warlike Man" - Cassius Dio's Perception and Interpretation of the Imperial Military persona / Wolfgang Havener -- The War Comes Home: Rome and Romans during Civil Conflict in the Roman History / Alex Imrie -- Talking Heads: the Rostra as a Conspicuous Civil War Monument / Carsten Hjort Lange --



Cassius Dio, Cicero and the Complexity of Civil War / Ayelet Peer -- Cassius Dio on Senatorial Activities as a Factor of Political Instability and Civil War / Konstantin V. Markov -- Cassius Dio and Senatorial Memory of Civil War in the 190s / Adam M. Kemezis -- Cassius Dio, and Civil War / Sulochana R. Asirvatham -- "If You Do Wrong, You Will Be King!": the Civil War Victor in Cassius Dio / Josiah Osgood -- Civil War and Governmental Change: From the Achievements of Augustus to the Failures of the Severans / Andrew G. Scott.

Sommario/riassunto

Cassius Dio: The Impact of Violence, War, and Civil War is part of a renewed interest in the Roman historian Cassius Dio. This volume focuses on Dio’s approaches to foreign war and stasis as well as civil war. The impact of war on Rome as well as on the history of Rome has long be recognised by scholars, and adding to that, recent years have seen an increasing interest in the impact of civil war on Roman society. Dio’s views on violence, war, and civil war are an inter-related part of his overall project, which sought to understand Roman history on its own historical and historiographical terms and within a long-range view of the Roman past that investigated the realities of power.