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This monograph studies an important generalisation of
the Cauchy integral formula, called the Dbar formula.
In particular, it investigates the
physical significance of this formula, its extension
to three, four and higher dimensions and the
applications of the relevant formalism to:
(i) The solution of boundary value problems for
linear partial differential equations ;
(ii) The evaluation of real integrals;
(iii) The construction of nonlinear integrable
equations starting from the corresponding linear
equations.
A large part of this monograph is devoted to the
theory of quaternions. It is shown that quaternions
provide the proper generalisation of complex numbers.
The book offers a pedagogical introduction to the
theory of quaternions and attempts to elucidate its
analytic component. Also, it presents some novel
applications of this theory.
This monograph will be useful to readers interested
in the theory and applications of quaternions from
the point of view of analysis as well as to everyone
interested in explicit solutions of boundary value
problems for partial differential equations.
the Cauchy integral formula, called the Dbar formula.
In particular, it investigates the
physical significance of this formula, its extension
to three, four and higher dimensions and the
applications of the relevant formalism to:
(i) The solution of boundary value problems for
linear partial differential equations ;
(ii) The evaluation of real integrals;
(iii) The construction of nonlinear integrable
equations starting from the corresponding linear
equations.
A large part of this monograph is devoted to the
theory of quaternions. It is shown that quaternions
provide the proper generalisation of complex numbers.
The book offers a pedagogical introduction to the
theory of quaternions and attempts to elucidate its
analytic component. Also, it presents some novel
applications of this theory.
This monograph will be useful to readers interested
in the theory and applications of quaternions from
the point of view of analysis as well as to everyone
interested in explicit solutions of boundary value
problems for partial differential equations.