Some remarks on monodromy
We consider hypoelliptic symbols over a very regular Lie group and discuss monodromy for a spectral stratification using results of Nilsson and B\"acklund.
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arXiv subjects
Tove Dahn
Publications and source records attributed to Tove Dahn.
Some remarks on monogenity
We discuss representations of monogenic functions over very regular groups.
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On uniformity for the polar to partially hypoelliptic operators
We discuss the polar in symbol space to hypoelliptic and partially hypoelliptic operators, assuming a transmission property related to a rectifiable boundary and using a representation based on two scalar products.
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On a weak Lie type for vectors
In the symbol space for differential operators, we discuss a scalar type for change of local coordinates, using vector valued distributions. In particular, we discuss P-convexity for hypoelliptic operators.
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Some remarks on vector valued distributions
We argue that the fundamental solution corresponding to a maximal rank differential operator, where the symbol is regarded as a vector valued distribution, is not necessarily very regular. Thus, for a fundamental solution, the property of being very regular, is not invariant to change of local coordinates.
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Some remarks on maximal rank
We argue that the spiral can, in presence of a maximum principle, be of maximal rank at a boundary, but does not preserve hypoellipticity.
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Some remarks on polar sets to sums of squares
We argue that a necessary condition for hypoellipticity is that the polar is not a spiral domain.
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Some remarks on mixed problems
I will attempt to represent a symbol to a ps.d.o., using two bases and a lifting functional. The representation is based upon an invariance principle and conditions on the boundary, defined by first surfaces to the symbol.
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On partially hypoelliptic operators. Part II: Pseudo differential operators
This study is an attempt at generalizing the class of partially hypoelliptic differential operators to a class of pseudodifferential operators, Symbol ideals are formed on the set of lineality and we discuss suitable topologies that allow the generalizations.
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On partially hypoelliptic operators. Part I: Differential operators
This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in ArXiv. Close to N. Nilsson "Some estimates for spectral functions connected with formally hypoelliptic differential operators" in Arkiv för matematik ,10, 1972, we give a construction and estimates for a fundamental solution to the operator in a suitable topology. We further give estimates of the corresponding spectral kernel.
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Some remarks on prediction models
This article is a discussion of some characteristic properties in connection with global models, particularly for the application of prediction, such as the approximation property, the interpolation property and the transmission property.
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Some remarks on Trèves' conjecture
I will give a discussion of the conditions involved in Treves' conjecture on analytic hypoellipticity. I will discuss some microlocally characteristic sets and introduce a topology of monotropic functionals as suitable for solving the conjecture. The pseudodifferential operator representation is inspired by Cousin.
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