a b s t r a c tThe fine spectra of lower triangular double-band matrices have been examined by several authors (e.g. [13,22]). Here we determine the fine spectra of upper triangular double-band matrices over the sequence spaces c 0 and c. Upper triangular double-band matrices are infinite matrices which include the left-shift, averaging and difference operators.
Using local interpolation of Whitney functions, we generalize the Pawłucki and Pleśniak approach to construct a continuous linear extension operator. We show the continuity of the modified operator in the case of generalized Cantor-type sets without Markov's Property.
Smoothness of the Green functions for the complement of rarefied Cantortype sets is described in terms of the function ϕ(δ) = (1/ log 1 δ ) that gives the logarithmic measure of sets. Markov's constants of the corresponding sets are evaluated.
The fine spectra of upper and lower triangular banded matrices were examined by several authors. Here we determine the fine spectra of tridiagonal symmetric infinite matrices and also give the explicit form of the resolvent operator for the sequence spaces c 0 , c, 1 , and ∞ .
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