Fourier Analysis on Starlike Lipschitz Surfaces
By Tao Qian. 2001
57 citations recorded by the source corpus.
A theory of a class of singular integrals on starlike Lipschitz surfaces in Rn is established. The class of singular integrals forms an operator algebra identical to the class of bounded holomorphic Fourier multipliers, as well as to the Cauchy–Dunford bounded holomorphic functional calculus of the spherical Dirac operator. The study proposes a new method inducing Clifford holomorphic functions from holomorphic functions of one complex variable, by means of which problems on the sphere are reduced to those on the unit circle.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/6317cd04cf197707525ca413b7f5a78b843881c3
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In Applied Mathematics
- Irene Sabadini
- Fabrizio Colombo
- F. Sommen
- Daniele C. Struppa
- Caterina Stoppato
- Graziano Gentili
- Daniel Alpay
- Riccardo Ghiloni
Citations in the corpus
- REMARKS ON THE GENERATION OF MONOGENIC FUNCTIONS (2006, background): “Due to the fact that the polynomials Pk are real-valued if they are restricted to the real line in its domain, they can also be characterized as intrinsic functions in R in the sense of Rinehart ([25, 26]), (see also Tao Qian ([21, 22]).”
- The inverse Fueter mapping theorem (2011, background): “The Fueter mapping theorem can be stated in differential form in various versions, see [24], [25], [26], [27], [28], [29], [30] and the literature therein.”
- The $H^\infty$ functional calculus based on the $S$-spectrum for quaternionic operators and for $n$-tuples of noncommuting operators (2015, unknown): “[39] and [40] and the references therein.”
- The Fueter mapping theorem in integral form and the ℱ‐functional calculus (2010, methodology): “Later on, Fueter’s theorem has been generalized to the case in which a function f as above is multiplied by a monogenic homogeneous polynomial of degree k, see [17--20] and to the case in which the function f is defined on an open set U not necessarily chosen in the upper complex plane, see [16, 21,”