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## Details

Document Type: | Book |
---|---|

All Authors / Contributors: |
Charles S Kahane; MINNESOTA UNIV MINNEAPOLIS SCHOOL OF MATHEMATICS. |

OCLC Number: | 227498983 |

Description: | 68 p. |

### Abstract:

The author studies the analyticity properties of solutions of the equation g = Kf where K is a singular integral operator of the Calderon-Zygmund type with g and f in L sub p. Assuming that g and K are locally analytic in a suitable sense and that the symbol of the operator K is locally not equal to 0, any solution of the equation g = Kf is shown to be locally analytic. This generalizes the well-known result that solutions of linear analytic elliptic partial differential equations are themselves analytic. (Author).

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## Similar Items

### Related Subjects:(15)

- Theoretical Mathematics.
- (Integral equations.
- Analytic functions)
- Operators(mathematics)
- Complex variables.
- Special functions(mathematical)
- Potential theory.
- Partial differential equations.
- Integral transforms.
- Fourier analysis.
- Theorems.
- ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS
- FOURIER TRANSFORMS
- SOLUTIONS(MATHEMATICS)
- SPHERICAL HARMONICS