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Let X be a compact Kähler manifold with strictly pseudoconvex boundary , Y. In this setting, the Spin C Dirac operator is canonically identified with ¯ ∂ + ¯ We consider modifications of the classical ¯ ∂-Neumann conditions that define Fredholm problems for the Spin C Dirac operator. In part 2, [7], we use boundary layer methods to obtain subel-liptic… (More)

- H. I. Epstein
- SYMSACC
- 1976

This paper describes a procedure for determining when a set of rational functions are pseudo-multiplicatively independent, i.e. when no non-trivial power product of the rational functions can be a constant. The method used is to derive a multiplicative basis of factors of the numerators and denominators of the rational functions; the basis is then used to… (More)

- H. I. Epstein, B. F. Caviness
- International Journal of Parallel Programming
- 1979

- B. F. Caviness, H. I. Epstein
- Inf. Process. Lett.
- 1977

It is a well-known empirical result that differentiation, especially higher order differentiation, of simple expressions can lead to long and complex expressions. In this paper we give some theoretical results that help to explain this phenomenon. In particular we show that in certain representations there exist expressions whose representations require… (More)

We begin a study of normal form theorems for parabolic partial diierential equations. We show that despite the presence of resonances one can construct a partial normal form for perturbations of the Ginzburg-Landau equation. The normal form transformation is expressed in terms of singular integral operators, whose behavior can be controlled in the… (More)

- H. I. Epstein
- SIAM J. Comput.
- 1979

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