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Supercomplex structures, surface soliton equations, and quasiconformal mappings

Julian Ławrynowicz;  Katarzyna Kędzia;  Osamu Suzuki — 1991

Annales Polonici Mathematici

Hurwitz pairs and triples are discussed in connection with algebra, complex analysis, and field theory. The following results are obtained: (i) A field operator of Dirac type, which is called a Hurwitz operator, is introduced by use of a Hurwitz pair and its characterization is given (Theorem 1). (ii) A field equation of the elliptic Neveu-Schwarz model of superstring theory is obtained from the Hurwitz pair (⁴,³) (Theorem 2), and its counterpart connected with the Hurwitz triple ( 11 , 11 , 26 ) is mentioned....

Differential and integral calculus for a Schauder basis on a fractal set (I) (Schauder basis 80 years after)

Julian Ławrynowicz;  Tatsuro Ogata;  Osamu Suzuki — 2009

Banach Center Publications

In this paper we introduce a concept of Schauder basis on a self-similar fractal set and develop differential and integral calculus for them. We give the following results: (1) We introduce a Schauder/Haar basis on a self-similar fractal set (Theorems I and I'). (2) We obtain a wavelet expansion for the L²-space with respect to the Hausdorff measure on a self-similar fractal set (Theorems II and II'). (3) We introduce a product structure and derivation on a self-similar fractal set (Theorem III)....

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