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On the fine spectrum of the generalized difference operator<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$B(r,s)$"><mml:mi>B</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>over the sequence spaces<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$c_0$"><mml:msub><mml:mi>c</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math>and<mml:math xmlns:mml="http://www.w3.…
We determine the fine spectrum of the generalized difference operator B ( r , s ) defined by a band matrix over the sequence spaces c 0 and c , and derive a Mercerian theorem. This generalizes our earlier work (2004) for the difference operator Δ , and includes as …