Titlebook: Liouville-Riemann-Roch Theorems on Abelian Coverings; Minh Kha,Peter Kuchment Book 2021 The Editor(s) (if applicable) and The Author(s), u

Obstruction

打火石

Minh Kha,Peter KuchmentThe first unified exposition of Liouville and Riemann–Roch type theorems for elliptic operators on abelian coverings.Gives a well-organized and self-contained exposition of the topic, including new re

Discrete

Lecture Notes in Mathematicshttp://image.papertrans.cn/l/image/586827.jpg

不如乐死去

The Main Results,, the Riemann-Roch type equalities cannot be achieved (counterexamples are shown), while inequalities still hold. These inequalities, however, can be applied, the same way the equalities are, for proving the existence of solutions of elliptic equations with prescribed zeros, poles, and growth at infinity.

强化

reptile

Specific Examples of Liouville-Riemann-Roch Theorems,In this chapter, we look at some examples of applications of the results of Chap. .. These include in particular self-adjoint operators with non-degenerate spectral band edges, operators with Dirac points in dispersion relation, as well as some non-self-adjoint cases.

Veneer

Auxiliary Statements and Proofs of Technical Lemmas,Here we collect a variety of technical auxiliary considerations and results used in, or related to the content of the main chapters of the book.

JAUNT

影响

情节剧

Gabriel Amaral,Mārcis Pinnis,Inguna Skadiņa,Odinaldo Rodrigues,Elena Simperlry material: .For the first time in limnofaunistic bibliography, the present taxonomic knowledge about the different clades of chelicerata having adapted to an aquatic or amphibious lifestyle along various evolutionary pathways is brought together in an overview for the Central-European fauna. A tot