Another session of the Nizhny Novgorod Mathematical Society has occured

On September 26, N. N. Shamarov's talk “Infinite-dimensional pseudo-differential operators for the second quantization method” has been presented.

At the picture: N.N. Shamarov

At the picture: N.N. Shamarov

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The purpose of the talk was to discuss the properties of infinite-dimensional pseudodifferential operators (BMPDOs), in particular, to examine the relationship between two new approaches to their determination. One of them relies only on the technique of countable additive measures, but at the same time uses the concept of the Kolmogorov integral. Another approach uses a generalized measure invariant under orthogonal affine transformations on a Hilbert space Q, similar to the Lebesgue measure (which, by virtue of A. Weil’s theorem, does not exist on infinite-dimensional spaces) and called the generalized Lebesgue measure.