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Articles

The C-property for slice regular functions and applications to the Bergman space

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Pages 1355-1372 | Received 17 May 2011, Accepted 05 Mar 2012, Published online: 16 Apr 2012

References

  • Colombo , F , González-Cervantes , JO , Luna-Elizarrarás , ME , Sabadini , I and Shapiro , M . 2011 . Formulations of the Bergman theories for slice regular functions, , preprint
  • Gentili , G and Struppa , DC . 2007 . A new theory of regular functions of a quaternionic variable . Adv. Math. , 216 : 279 – 301 .
  • Colombo , F , Sabadini , I and Struppa , DC . 2009 . Slice monogenic functions . Israel J. Math. , 171 : 385 – 403 .
  • Colombo , F , Sabadini , I and Struppa , DC . 2011 . Noncommutative Functional Calculus, Theory and Applications of Slice Hyperholomorphic Functions , Vol. 289 , Birkhäuser, Basel : Progress in Mathematics .
  • Ghiloni , R and Perotti , A . 2011 . A new approach to slice regularity on real algebras . Adv. Math. , 226 : 1662 – 1691 .
  • Bergman , S . 1970 . The Kernel Function and Conformal Mapping , Providence , , RI : American Mathematical Society .
  • Bergman , S and Schiffer , M . 1953 . Kernel Functions and Elliptic Differential Equations in Mathematical Physics , New York : Academic Press .
  • Brackx , F and Delanghe , R . 1978 . Hypercomplex function theory and Hilbert modules with reprocucing kernel . Proc. Amer. Math. Soc. , 37 : 545 – 576 .
  • Brackx , F , Delanghe , R and Sommen , F . 1982 . “ Clifford Analysis ” . In Pitman Research Notes in Mathematics , Vol. 76 , Boston : Pitman .
  • Constales , D . 1990 . The Bergman and Szegö kernels for separately monogenic functions . Zeit. Anal. Anwen. , 9 : 97 – 103 .
  • Constales , D and Kraußhar , RS . 2002 . Bergman kernels for rectangular domains and multiperiodic functions in Clifford analysis . Math. Meth. Appl. Sci. , 25 : 1509 – 1526 .
  • Constales , D and Kraußhar , RS . 2006 . Bergman spaces of higher-dimensional hyperbolic polyhedron-type domains I . Math. Meth. Appl. Sci. , 29 : 85 – 98 .
  • Delanghe , R . 1976 . On Hilbert modules with reproducing kernel . Lecture Notes in Math. , 561 : 158 – 170 .
  • González-Cervantes , JO , Luna-Elizarrarás , ME and Shapiro , M . 2009 . On some categories and functors in the theory of quaternionic Bergman spaces . Adv. Appl. Clifford Algebras , 19 : 325 – 338 .
  • Shapiro , M and Vasilevski , N . 1977 . On the Bergman kernel function in hyperholomorphic analysis . Acta Appl. Math. , 46 : 1 – 27 .
  • Shapiro , M and Vasilevski , N . On the Bergman kernel function in Clifford analysis, Fund. Theories Phys., 55 (1993), pp. 183–192
  • Shapiro , M and Vasilevski , N . 1998 . On the Bergman kernel functions in quaternionic analysis . Russian Math. , 42 : 81 – 85 .
  • Colombo , F , González-Cervantes , JO and Sabadini , I . 2011 . A non-constant coefficient differential operator associated to slice monogenic functions . preprint
  • Krantz , SG . 1982 . Function Theory of Several Complex Variables , 2nd , Pacific Grove, CA : Wadsworth & Brooks .
  • Colombo , F and Sabadini , I . 2009 . “ A structure formula for slice monogenic functions and some of its consequences ” . In Hypercomplex Analysis , Edited by: Sabadini , I , Shapiro , M and Sommen , F . 101 – 114 . Birkhäuser, Basel : Trends in Mathematics .
  • Colombo , F , Sabadini , I and Struppa , DC . Sheaves of slice regular functions . Math. Nach , (to appear). DOI: 10.1002/mana.201000149

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