The dual of the space of holomorphic functions on locally closed convex sets

Let H(Q) be the space of all the functions which are holomorphic on an open neighbourhood of a convex locally closed subset Q of CN , endowed with its natural projective topology. We characterize when the topology of the weighted inductive limit of Fréchet spaces which is obtained as the Laplace transform of the dual H(Q) 0 of H(Q) can be described by weighted sup-seminorms. The behaviour of the corresponding inductive limit of spaces of continuous functions is also investigated

Each non-zero convolution operator on the entire functions admits a continuous linear right inverse

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46274/1/209_2005_Article_BF01161635.pd

Investigating Speaker Embedding Disentanglement on Natural Read Speech

Disentanglement is the task of learning representations that identify and separate factors that explain the variation observed in data. Disentangled representations are useful to increase the generalizability, explainability, and fairness of data-driven models. Only little is known about how well such disentanglement works for speech representations. A major challenge when tackling disentanglement for speech representations are the unknown generative factors underlying the speech signal. In this work, we investigate to what degree speech representations encoding speaker identity can be disentangled. To quantify disentanglement, we identify acoustic features that are highly speaker-variant and can serve as proxies for the factors of variation underlying speech. We find that disentanglement of the speaker embedding is limited when trained with standard objectives promoting disentanglement but can be improved over vanilla representation learning to some extent.Comment: To be published at 15th ITG conference on speech communicatio

Right inverses for linear, constant coefficient partial differential operators on distributions over open half spaces

Results of Hörmander on evolution operators together with a characterization of the present authors [Ann. Inst. Fourier, Grenoble 40, 619 – 655 (1990)] are used to prove the following: Let and denote by its principal part. If is dominated by then the following assertions for the partial differential operators and are equivalent for :¶¶(1)  and/or admit a continuous linear right inverse on .¶(2)  admits a continuous linear right inverse on and a fundamental solution satisfying Supp ,¶where 0} $]]> .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41826/1/13-68-4-311_70680311.pd

On the theorem of Borel for quasianalytic classes

[EN] We investigate the surjectivity of the Borel map in the quasianalytic setting for classes of ultradifferentiable functions defined in terms of the growth of the Fourier-Laplace transform. We deal with both the Roumieu E{ω} and the Beurling E(ω) classes for a weight function ω. In particular, we show that a classical result of Carleman for the quasianalytic classes E{Mp} also holds for the classes defined using weights. We also characterize when the space of quasianalytic germs at the origin coincides with the space of real analytic germs at the originThe research of Bonet was partially supported by MEC and FEDER Project MTM2010-15200 and by GV Project Prometeo /2008/101.Bonet Solves, JA.; Meise, R. (2013). On the theorem of Borel for quasianalytic classes. Mathematica Scandinavica. 112(2):302-319. https://doi.org/10.7146/math.scand.a-15246S302319112

The algebraic surfaces on which the classical Phragmén-Lindelöf theorem holds

Let V be an algebraic variety in . We say that V satisfies the strong Phragmén-Lindelöf property (SPL) or that the classical Phragmén-Lindelöf Theorem holds on V if the following is true: There exists a positive constant A such that each plurisubharmonic function u on V which is bounded above by | z |+ o (| z |) on V and by 0 on the real points in V already is bounded by A | Im z |. For algebraic varieties V of pure dimension k we derive necessary conditions on V to satisfy (SPL) and we characterize the curves and surfaces in which satisfy (SPL). Several examples illustrate how these results can be applied.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46283/1/209_2005_Article_913.pd

Whitney’s extension theorem for ultradifferentiable functions of Beurling type

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43941/1/11512_2006_Article_BF02386123.pd