# Differential operators of the first order with degenerate principal symbols

Banach Center Publications (1992)

- Volume: 27, Issue: 1, page 147-161
- ISSN: 0137-6934

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topFelix, Rainer. "Differential operators of the first order with degenerate principal symbols." Banach Center Publications 27.1 (1992): 147-161. <http://eudml.org/doc/262773>.

@article{Felix1992,

abstract = {Let there be given a differential operator on $ℝ^n$ of the form $D = ∑^\{n\}_\{i,j=1\} a_\{ij\}·x_j ∂/∂x_i + μ$, where $A = (a_\{ij\})$ is a real matrix and μ is a complex number. We study the following question: To what extent the mapping $D :S^\{\prime \}(ℝ^n) → S^\{\prime \}(ℝ^n)$ is surjective? We shall give some conditions on A and μ which assure the surjectivity of D.},

author = {Felix, Rainer},

journal = {Banach Center Publications},

keywords = {Schwartz space},

language = {eng},

number = {1},

pages = {147-161},

title = {Differential operators of the first order with degenerate principal symbols},

url = {http://eudml.org/doc/262773},

volume = {27},

year = {1992},

}

TY - JOUR

AU - Felix, Rainer

TI - Differential operators of the first order with degenerate principal symbols

JO - Banach Center Publications

PY - 1992

VL - 27

IS - 1

SP - 147

EP - 161

AB - Let there be given a differential operator on $ℝ^n$ of the form $D = ∑^{n}_{i,j=1} a_{ij}·x_j ∂/∂x_i + μ$, where $A = (a_{ij})$ is a real matrix and μ is a complex number. We study the following question: To what extent the mapping $D :S^{\prime }(ℝ^n) → S^{\prime }(ℝ^n)$ is surjective? We shall give some conditions on A and μ which assure the surjectivity of D.

LA - eng

KW - Schwartz space

UR - http://eudml.org/doc/262773

ER -

## References

top- [1] R. Felix, Solvability of differential equations with linear coefficients of nilpotent type, Proc. Amer. Math. Soc. 94 (1985), 161-166. Zbl0541.35010
- [2] R. Felix, Zentrale Distributionen auf Exponentialgruppen, J. Reine Angew. Math. 389 (1988), 133-156.
- [3] G. B. Folland, Real Analysis. Modern Techniques and Their Applications, Wiley, New York 1984. Zbl0549.28001
- [4] L. Hörmander, On the division of distributions by polynomials, Ark. Mat. 3 (1958), 555-568. Zbl0131.11903
- [5] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, Berlin 1983. Zbl0521.35001
- [6] D. Müller and F. Ricci, Analysis of second order differential operators on Heisenberg groups II, preprint. Zbl0790.43011
- [7] H. H. Schaefer, Topological Vector Spaces, 5th printing, Springer, New York 1986.
- [8] L. Schwartz, Théorie des distributions, Hermann, Paris 1966.

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