# Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse

B. A. Taylor; R. Meise; Dietmar Vogt

Annales de l'institut Fourier (1990)

- Volume: 40, Issue: 3, page 619-655
- ISSN: 0373-0956

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topTaylor, B. A., Meise, R., and Vogt, Dietmar. "Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse." Annales de l'institut Fourier 40.3 (1990): 619-655. <http://eudml.org/doc/74890>.

@article{Taylor1990,

abstract = {Solving a problem of L. Schwartz, those constant coefficient partial differential operators $P(D)$ are characterized that admit a continuous linear right inverse on $\{\cal E\}(\Omega )$ or $\{\cal D\}^\{\prime \}(\Omega )$, $\Omega $ an open set in $\{\bf R\}^ n$. For bounded $\Omega $ with $C^ 1$-boundary these properties are equivalent to $P(D)$ being very hyperbolic. For $\Omega =\{\bf R\}^n$ they are equivalent to a Phragmen-Lindelöf condition holding on the zero variety of the polynomial $P$.},

author = {Taylor, B. A., Meise, R., Vogt, Dietmar},

journal = {Annales de l'institut Fourier},

keywords = {constant coefficient partial differential operators; continuous linear right inverse; Phragmén-Lindelöf condition},

language = {eng},

number = {3},

pages = {619-655},

publisher = {Association des Annales de l'Institut Fourier},

title = {Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse},

url = {http://eudml.org/doc/74890},

volume = {40},

year = {1990},

}

TY - JOUR

AU - Taylor, B. A.

AU - Meise, R.

AU - Vogt, Dietmar

TI - Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse

JO - Annales de l'institut Fourier

PY - 1990

PB - Association des Annales de l'Institut Fourier

VL - 40

IS - 3

SP - 619

EP - 655

AB - Solving a problem of L. Schwartz, those constant coefficient partial differential operators $P(D)$ are characterized that admit a continuous linear right inverse on ${\cal E}(\Omega )$ or ${\cal D}^{\prime }(\Omega )$, $\Omega $ an open set in ${\bf R}^ n$. For bounded $\Omega $ with $C^ 1$-boundary these properties are equivalent to $P(D)$ being very hyperbolic. For $\Omega ={\bf R}^n$ they are equivalent to a Phragmen-Lindelöf condition holding on the zero variety of the polynomial $P$.

LA - eng

KW - constant coefficient partial differential operators; continuous linear right inverse; Phragmén-Lindelöf condition

UR - http://eudml.org/doc/74890

ER -

## References

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