English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This article can be considered as the first version of a book which theauthor plans to write about half-range problems in operator theory. It consistsof two parts. The first part is based on lectures which the author delivered atUniversity of Calgary and Lomonosov Moscow State University. The main attentionin this part is paid to the selection of waves which are involved in theformulation of the Mandelstamm radiation principle (the eigen-pairs,corresponding to the real eigenvalues) and to the factorization problems ofself-adjoint and dissipative, quadratic and polynomial operator pencils. Thereis a dramatic difference between finite dimensional and infinite dimensionalcases. It is shown that in the finite dimensional case the factorizationproblems can be solved completely. In the second part we consider abstractmodels for concrete problems of mechanics. We demonstrate the methods howconcrete problems can be represented in an abstract form. The main resultsconcern the factorization of elliptic operator pencils satisfying the resolventgrowth condition in a double sector containing the real axis and theinvestigation of the semi-group properties of a divisor. Using Pontrjagin spacemethods we obtain a criterium for the stability in the celebrated Sobolevproblem about a rotating top with a cavity filled with a viscous liquid.

Operator Pencils and Half-range Problem in Operator Theory