# Second term of the spectral asymptotic expansion of the Laplace - Beltrami operator on manifolds with boundary

@article{Ivrii1980SecondTO,
title={Second term of the spectral asymptotic expansion of the Laplace - Beltrami operator on manifolds with boundary},
author={Victor Ivrii},
journal={Functional Analysis and Its Applications},
year={1980},
volume={14},
pages={98-106}
}
• V. Ivrii
• Published 1980
• Mathematics
• Functional Analysis and Its Applications
A weld head control and guidance system utilizing non-contact proximity sensors which generate a signal based on the electrical conductivity of a workpiece. The system includes electrical controls which receive the signal generated by the proximity sensors and control movement of a movable torch mount to maintain a welding torch in a proper orientation and position with respect to a workpiece.
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#### References

SHOWING 1-9 OF 9 REFERENCES
The spectral function of an elliptic operator
In this paper we shall obtain the best possible estimates for the remainder term in the asymptotic formula for the spectral function of an arbitrary elliptic (pseudo-)differential operator. This isExpand
The spectrum of positive elliptic operators and periodic bicharacteristics
• Mathematics
• 1975
Let X be a compact boundaryless C ∞ manifold and let P be a positive elliptic self-adjoint pseudodifferential operator of order m>0 on X. For technical reasons we will assume that P operates onExpand
Fourier integral operators. I
Pseudo-differential operators have been developed as a tool for the study of elliptic differential equations. Suitably extended versions are also applicable to hypoelliptic equations, but their valueExpand