Reiterative $m_{n}$-distributional chaos of type $s$ in Fr\' echet spaces

DOI10.1007/S40840-020-00906-XarXiv1902.03474MaRDI QIDQ6313851

Publication date: 9 February 2019

Abstract: The main aim of this paper is to consider various notions of (dense)

m_{n}

-distributional chaos of type

s

and (dense) reiterative

m_{n}

-distributional chaos of type

s

for general sequences of linear not necessarily continuous operators in Fr' echet spaces. Here,

(m_{n})

is an increasing sequence in

[1, i n f t y)

satisfying

l i m i n f_{n i g h t a r r o w i n f t y} f r a c m_{n} n > 0

and

s

could be

0, 1, 2, 2 +, 2 f r a c 12, 3, 1 +, 2 -, 2_{B d}, 2_{B d} + .

We investigate

m_{n}

-distributionally chaotic properties and reiteratively

m_{n}

-distributionally chaotic properties of some special classes of operators like weighted forward shift operators and weighted backward shift operators in Fr' echet sequence spaces, considering also continuous analogues of introduced notions and some applications to abstract partial differential equations.

Mathematics Subject Classification ID

Linear relations (multivalued linear operators) (47A06) Cyclic vectors, hypercyclic and chaotic operators (47A16)

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