Málstofa í stærðfræði

### Fyrirlesari: Arkadiusz Lewandowski, University of Iceland Titill: Separate vs joint regularity of functions

Staðsetning: V-157, VRII
Tími: Mánudagur 3. nóvember, frá 15:00 til 16:00.

### Ágrip:

Consider the following problem:
Given two domains $$D \subset K^p, G \subset K^q$$, where $$K$$ equals either $$\mathbb R$$ or $$\mathbb C$$, and a function $$f$$ on the product $$D \times G$$, taking complex values, and such that:
1. $$f(a,-)$$ is in $$F(G)$$, for any $$a$$ in $$D$$,
2. $$f(-,b)$$ is in $$F(D)$$, for any $$b$$ in $$G$$,
we ask whether $$f$$ is in $$F(D\times G)$$.
Here for any open set $$U$$ in any $$K^n, F(U)$$ is some abstract family of functions.
We shall discus the cases $$F \in \{\mathcal{C,O,H,SH}\}$$, where $$\mathcal C$$ denotes the family of continuous functions, $$\mathcal O$$ is the family of holomorphic functions, $$\mathcal H$$ stands for the family of harmonic functions, and $$\mathcal{SH}$$ – the family of subharmonic functions. Math Colloquium

### Speaker: Arkadiusz Lewandowski, University of Iceland Title: Separate vs joint regularity of functions

Location: V-157, VRII
Time: Monday, November 3 at 15:00-16:00.

### Abstract:

Consider the following problem:
Given two domains $$D \subset K^p, G \subset K^q$$, where $$K$$ equals either $$\mathbb R$$ or $$\mathbb C$$, and a function $$f$$ on the product $$D \times G$$, taking complex values, and such that:
1. $$f(a,-)$$ is in $$F(G)$$, for any $$a$$ in $$D$$,
2. $$f(-,b)$$ is in $$F(D)$$, for any $$b$$ in $$G$$,
we ask whether $$f$$ is in $$F(D\times G)$$.
Here for any open set $$U$$ in any $$K^n, F(U)$$ is some abstract family of functions.
We shall discus the cases $$F \in \{\mathcal{C,O,H,SH}\}$$, where $$\mathcal C$$ denotes the family of continuous functions, $$\mathcal O$$ is the family of holomorphic functions, $$\mathcal H$$ stands for the family of harmonic functions, and $$\mathcal{SH}$$ – the family of subharmonic functions.