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Seminar on analysis and geometry

Analysis and geometry seminar is held usually on **Wednesdays at 12-14 **in **M3**.

Organizers:

Organizers:

Harmonic analysis and PDE seminar

As of January 2016, we launched a joint seminar of the Harmonic Analysis group at the University of Helsinki, and the Nonlinear PDE group at the Aalto University.

Starting from fall 2017, we have a new schedule. The seminar is held once in 3 weeks but with two one-hour talks. The time is the same as before **Fridays at 14-16.** The place alternates between the University of Helsinki Kumpula Campus (Exactum room **C124**) and the Aalto University Otaniemi Campus (Main Building room **M3**).

Everyone interested is welcome!

Organizers:

Organizers:

See the webpage of the seminar. The talks are listed in the end of this page as well.

- 17.10. 12:15 Vasiliki Evdoridou (The Open University, UK): Singularities of inner functions and entire maps of finite order – M3 (M234)
Let f be a transcendental entire function of finite order and U an unbounded, invariant Fatou component of f. We can associate an inner function, g say, to the restriction of f to U. We will show that for two classes of entire functions whose set of singular values is bounded, the number of singularities of g on the unit circle is at most twice the order of f. This is joint work with N. Fagella, X. Jarque and D. Sixsmith.

- 24.10. 12:15 Hans Tylli (University of Helsinki): Structural rigidity of generalised Volterra operators on Hardy spaces – M3 (M234)
will describe generalised analytic Volterra operators T_g on the Hardy spaces H^p over the unit disk D for 1 \le p < \infty, where T_gf(z) = \int_0^z f(w)g'(w) dw, for z in D and f in H^p. Above the analytic map g from BMOA is the symbol of T_g. The systematic study of this class of operators was initiated by Aleman, Cima and Siskakis around 1995. Earlier certain T_g were used by Pommerenke (1977) and the class contains e.g. a version of the classical Cesaro averaging operator, which is obtained with g(z) = - \log(1-z). I will focus attention on recent work on the structural rigidity of the class of non-compact operators T_g on H^p for p different from 2. The main result says that if T_g defines an isomorphism from M to T_g(M) for the infinite-dimensional closed subspace M of H^p, then M contains a subspace linearly isomorphic to the sequence space \ell^p. In particular, this implies that the non-compact Volterra operators T_g have a quite restricted range of linear qualitative behaviour compared to that of arbitrary bounded operators on H^p (for p different from 2). This is joint work with Santeri Miihkinen (Åbo), Pekka Nieminen (Turku) and Eero Saksman (Helsinki).

- 31.10. 12:15 Ratan Kumar Giri: Singular Nonlocal Problem Involving Measure Data – M3 (M234)
- 7.11. 12:15 Vito Buffa (University of Ferrara): BV Functions in Metric Measure Spaces: Traces and Integration by Parts Formulæ – M3 (M234)
We adapt the tools from the differential structure developed by N. Gigli in order to give a definition of BV functions on RCD(K,\infty) spaces via suitable vector fields and then establish an extended Gauss-Green formula on a class of "regular" domains, which features the "normal trace" of vector fields with finite divergence measure. Then, we pass to the more classical context of a doubling metric measure space supporting a Poincaré inequality, where we reformulate the theory of "rough traces" of BV functions (after V. Maz'ya) in comparison with the Lebesgue-points characterization, and discuss the conditions under which the respective notions of trace coincide. Based on a joint work with M. Miranda Jr.

- 14.11. 12:15 Karl Brustad (NTNU, Trondheim): The dominative p-Laplacian and sublinear elliptic operators – M3 (M234)
- 21.11. 12:15 Aleksis Koski (University of Jyväskylä): TBA – M3 (M234)

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