One Class of Linearly Growing C0-Groups

Автор(и)

  • Grigory Sklyar Institute of Mathematics, University of Szczecin, Szczecin, Poland
  • Vitalii Marchenko B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
  • Piotr Polak Institute of Mathematics, University of Szczecin, Szczecin, Poland

DOI:

https://doi.org/10.15407/mag17.04.509

Ключові слова:

C0-група, лiнiйне зростання, максимальна асимптотика, XYZ теорема

Анотація

Ми розглядаємо спецiальний клас C0-груп з [12], генератори яких є необмеженими, мають чисто точковий уявний спектр та вiдповiдну щiльну i мiнiмальну сiм’ю власних векторiв, яка, проте, не утворює базис Шаудера. Ми одержуємо двостороннi оцiнки норм C0- груп з цього класу i таким чином доводимо, що цi C0-групи зростають лiнiйно. Крiм того, ми доводимо, що C0-групи з класу, що розглядається, не мають жодної максимальної асимптотики. Це означає, що не iснує орбiти, що зростає найшвидше.

Mathematics Subject Classification: 47D06, 34G10, 46B45, 34K25

Посилання

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Sklyar, G.; Marchenko, V.; Polak, P. One Class of Linearly Growing C0-Groups. Журн. мат. фіз. анал. геом. 2021, 17, 509-520.

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