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The present paper is a continuation of [5, 7] where a Fredholm theory for approximation sequences is proposed and some of its properties and consequences are studied. Here this theory is specified to the class of fractal approximation methods. The main result is a formula for the so-called α-number of an approximation sequence (Aₙ) which is the analogue of the kernel dimension of a Fredholm operator.
Steffen Roch. "Algebras of approximation sequences: Fredholm theory in fractal algebras." Studia Mathematica 150.1 (2002): 53-77. <http://eudml.org/doc/285095>.
@article{SteffenRoch2002, abstract = {The present paper is a continuation of [5, 7] where a Fredholm theory for approximation sequences is proposed and some of its properties and consequences are studied. Here this theory is specified to the class of fractal approximation methods. The main result is a formula for the so-called α-number of an approximation sequence (Aₙ) which is the analogue of the kernel dimension of a Fredholm operator.}, author = {Steffen Roch}, journal = {Studia Mathematica}, keywords = {Fredholm theory; fractal algebra; compact sequences}, language = {eng}, number = {1}, pages = {53-77}, title = {Algebras of approximation sequences: Fredholm theory in fractal algebras}, url = {http://eudml.org/doc/285095}, volume = {150}, year = {2002}, }
TY - JOUR AU - Steffen Roch TI - Algebras of approximation sequences: Fredholm theory in fractal algebras JO - Studia Mathematica PY - 2002 VL - 150 IS - 1 SP - 53 EP - 77 AB - The present paper is a continuation of [5, 7] where a Fredholm theory for approximation sequences is proposed and some of its properties and consequences are studied. Here this theory is specified to the class of fractal approximation methods. The main result is a formula for the so-called α-number of an approximation sequence (Aₙ) which is the analogue of the kernel dimension of a Fredholm operator. LA - eng KW - Fredholm theory; fractal algebra; compact sequences UR - http://eudml.org/doc/285095 ER -