1.

Record Nr.

UNINA9910915795003321

Autore

Bruggeman Roelof

Titolo

Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume

Pubbl/distr/stampa

Providence : , : American Mathematical Society, , 2023

©2023

ISBN

1-4704-7539-1

Edizione

[1st ed.]

Descrizione fisica

1 online resource (186 pages)

Collana

Memoirs of the American Mathematical Society Series ; ; v.287

Classificazione

11F1211F6737C3011F7230F3537D40

Altri autori (Persone)

PohlAnke Dorothea

Disciplina

512.7

Soggetti

Automorphic forms

Transfer operators

Hecke algebras

Number theory -- Discontinuous groups and automorphic forms -- Automorphic forms, one variable

Number theory -- Discontinuous groups and automorphic forms -- Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols

Dynamical systems and ergodic theory -- Smooth dynamical systems: general theory -- Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems

Number theory -- Discontinuous groups and automorphic forms -- Spectral theory; Selberg trace formula

Functions of a complex variable -- Riemann surfaces -- Fuchsian groups and automorphic functions

Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

Cover -- Title page -- Chapter 1. Introduction -- Motivational background -- Aim of this monograph -- Acknowledgement -- Part 1. Preliminaries, properties of period functions, and some insights -- Chapter 2. Notations -- Chapter 3. Elements from hyperbolic geometry -- 3.1. Models and isometries -- 3.2. Classification of isometries -- 3.3. Cusps, funnels, limit set, and ordinary points -- 3.4. Geodesics,



resonances, and the Selberg zeta function -- 3.5. Intervals and rounded neighborhoods -- Chapter 4. Hecke triangle groups with infinite covolume -- Chapter 5. Automorphic forms -- 5.1. Funnel forms of different types -- 5.2. Fourier expansion -- Chapter 6. Principal series -- 6.1. Regularity at infinity -- 6.2. Presheaves and sheaves -- 6.3. Holomorphic extensions -- Chapter 7. Transfer operators and period functions -- 7.1. Discretizations and transfer operators -- 7.2. Slow transfer operators -- 7.3. Period functions -- 7.4. Real and complex period functions -- 7.5. Fast transfer operators -- 7.6. One-sided averages -- 7.7. Convergence and meromorphic extension of fast transfer operators -- 7.8. Spaces of complex period functions -- Chapter 8. An intuition and some insights -- Part 2. Semi-analytic cohomology -- Chapter 9. Abstract cohomology spaces -- 9.1. Standard group cohomology -- 9.2. Cohomology on an invariant set -- 9.3. Relation to parabolic cohomology spaces -- Chapter 10. Modules -- 10.1. Modules of semi-analytic functions -- 10.2. Submodules of semi-analytic vectors -- 10.3. Conditions on cocycles -- 10.4. Cohomological interpretation of the singularity condition -- Part 3. Automorphic forms and cohomology -- Chapter 11. Invariant eigenfunctions via a group cohomology -- Chapter 12. Tesselation cohomology -- 12.1. Choice of a tesselation, and cohomology -- 12.2. Relation to group cohomology -- 12.3. Mixed cohomology spaces.

Chapter 13. Extension of cocycles -- Chapter 14. Surjectivity I: Boundary germs -- 14.1. Analytic boundary germs and semi-analytic modules -- 14.2. Cohomology classes attached to funnel forms -- 14.3. Representatives of boundary germs -- Chapter 15. Surjectivity II: From cocycles to funnel forms -- 15.1. From a cocycle to an invariant eigenfunction -- 15.2. A cocycle on an orbit of ordinary points -- 15.3. Isomorphisms -- Chapter 16. Relation between cohomology spaces -- Chapter 17. Proof of Theorem D -- From funnel forms to cocycle classes on the invariant set -- From cocycle classes on to funnel forms -- Proof of Theorem D -- Part 4. Transfer operators and cohomology -- Chapter 18. The map from functions to cocycles -- Chapter 19. Real period functions and semi-analytic cocycles -- Chapter 20. Complex period functions and semi-analytic cohomology -- Chapter 21. Proof of Theorem E -- Part 5. Proofs of Theorems A and B, and a recapitulation -- Part 6. Parity -- Chapter 22. The triangle group in the projective general linear group -- 22.1. Two actions of the projective general linear group -- 22.2. The triangle group -- Chapter 23. Odd and even funnel forms, cocycles, and period functions -- 23.1. Odd and even funnel forms -- 23.2. Odd and even cocycles -- 23.3. Odd and even period functions -- Chapter 24. Isomorphisms with parity -- Part 7. Complements and outlook -- Chapter 25. Fredholm determinant of the fast transfer operator -- Chapter 26. Outlook -- Bibliography -- Index of terminology -- List of notations -- Back Cover.

Sommario/riassunto

"We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume and the dynamics of their geodesic flows"--



2.

Record Nr.

UNINA9910485141603321

Autore

Prifti Viola

Titolo

The Breeder's Exception to Patent Rights : Analysis of Compliance with Article 30 of the TRIPS Agreement / / by Viola Prifti

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015

ISBN

3-319-15771-X

Edizione

[1st ed. 2015.]

Descrizione fisica

1 online resource (195 p.)

Collana

International Law and Economics, , 2364-1851

Disciplina

330

330.1

340

340.2

340.9

343099

581.7

Soggetti

Mass media

Law

Commercial law

Plant ecology

Conflict of laws

Economics

IT Law, Media Law, Intellectual Property

Business Law

Plant Ecology

Private International Law, International & Foreign Law, Comparative Law

Economic Theory/Quantitative Economics/Mathematical Methods

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

Chapter 1: Setting the background -- Chapter 2: The industry of plant breeding -- Chapter 3: Intellectual Property in plant breeding -- Chapter 4: Conceptualizing the breeding exception to patent rights: a legal and economic appraisal -- Chapter 5: The breeding exception to patent rights: analysis of compliance with article 30 of the TRIPS



Agreement -- Chapter 6: Overview.

Sommario/riassunto

This book is the first to analyze the compliance of different types of a breeder's exception to patent rights with article 30 of the Agreement on Trade-Related Aspects of Intellectual Property Rights. This type of exception allows using protected biological matter for breeding new varieties of plants. The breeder’s exception is widely accepted under plant variety legislation, but it is not common under patent laws despite the fact that patent rights often cover plant varieties. Only few European countries have adopted such an exception. After the entry into force of the Agreement on a Unified Patent Court, the exception will be mandatory for all European Union Member states. Based on a legal and economic approach, this book offers guidance to those countries that need to incorporate a breeder's exception into their national patent systems and suggests the importance of the exception for promoting plant breeding activities.