### Program v akademickém roce 2021/2022

5. 5. 2022, 10:00

Somnath Hazra, An introduction to homogeneous operators.

19. 4. 2022, 13:00

Petr Blaschke, Level curves, inverse functions and multiple saddle point method.

7. 4. 2022, 10:00

Miroslav Engliš, Quantization and reproducing kernels - an excursion.

22. 3. 2022, 13:00

Noè Angelo Caruso, Krylov-solvability of inverse linear problems on Hilbert space.

25. 11. 2021, 11:25 - 12:10

Jaroslav Bradík, Calculating weighted harmonic Bergman kernel and asymptotic expansion of the harmonic Berezin transform on half-space.

4. 11. 2021, 11:25 - 12:10

Somnath Hazra, Homogeneous operators in the Cowen-Douglas class over the Poly-disc.

21. 10. 2021, 9:25 - 10:10

Miroslav Engliš, Balanced metrics on complex domains.

30. 9. 2021, 11:25 - 12:10

Petr Blaschke, Hypergeometrization.

Abstract:
We will introduce and discuss properties of "hypergeometrization", i.e. an operator acting on smooth functions given by
$$f\left(\begin{array}{c} a \\ c \end{array};x\right):=\sum_{k=0}^{\infty}\frac{f^{(k)}(x)}{k!} \frac{(c-a)_k}{(c)_k}(-x)^k,$$
where $c$, $a$ are given numbers and $f$ is a smooth function.

Generalized hypergeometric functions and their multivariate generalization can obtained by successive application of this operator on elementary functions. Hypergeometrization also converts an elementary identity into transformation rule of special functions. Finally, properties of the operator can link together many seemingly disconnected identities. For instance, from a single property of hypergeometrization (a special case of change of variable) we can deduce Pfaff transform, quadratic transform of 2F1, reduction of Appell˙s F1 to 3F2 and to 2F1, link between G2 and F1 functions and many more.