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# Documents  46-XX | enregistrements trouvés : 3

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## Post-edited  Mathematical and numerical aspects of frame theory - Part 1 Feichtinger, Hans G. (Auteur de la Conférence) | CIRM (Editeur )

Motivated by the spectrogram (or short-time Fourier transform) basic principles of linear algebra are explained, preparing for the more general case of Gabor frames in time-frequency analysis. The importance of the singular value decomposition and the four spaces associated with a matrix is pointed out, and based on this the pseudo-inverse (leading later to the dual Gabor frame) and the Loewdin (symmetric) orthogonalization are explained.
CIRM - Chaire Jean-Morlet 2014 - Aix-Marseille Université
Motivated by the spectrogram (or short-time Fourier transform) basic principles of linear algebra are explained, preparing for the more general case of Gabor frames in time-frequency analysis. The importance of the singular value decomposition and the four spaces associated with a matrix is pointed out, and based on this the pseudo-inverse (leading later to the dual Gabor frame) and the Loewdin (symmetric) orthogonalization are explained.
CIRM - ...

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## Multi angle  Mathematical and numerical aspects of frame theory - Part 2 Feichtinger, Hans G. (Auteur de la Conférence) | CIRM (Editeur )

Motivated by the spectrogram (or short-time Fourier transform) basic principles of linear algebra are explained, preparing for the more general case of Gabor frames in time-frequency analysis. The importance of the singular value decomposition and the four spaces associated with a matrix is pointed out, and based on this the pseudo-inverse (leading later to the dual Gabor frame) and the Loewdin (symmetric) orthogonalization are explained.
CIRM - Chaire Jean-Morlet 2014 - Aix-Marseille Université
Motivated by the spectrogram (or short-time Fourier transform) basic principles of linear algebra are explained, preparing for the more general case of Gabor frames in time-frequency analysis. The importance of the singular value decomposition and the four spaces associated with a matrix is pointed out, and based on this the pseudo-inverse (leading later to the dual Gabor frame) and the Loewdin (symmetric) orthogonalization are explained.
CIRM - ...

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## Multi angle  Norm-preserving extensions of bounded holomorphic functions McCarthy, John (Auteur de la Conférence) | CIRM (Editeur )

Let $V$ be an analytic subvariety of a domain $\Omega$ in $\mathbb{C}^{n}$. When does $V$ have the property that every bounded holomorphic function $f$ on $V$ has an extension to a bounded holomorphic function on $\Omega$ with the same norm?
An obvious sufficient condition is if $V$ is a holomorphic retract of $\Omega$. We shall discuss for what domains $\Omega$ this is also necessary.
This is joint work with Łukasz Kosiński.

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