Who developed one of the foundations of functional analysis and also taught Hugo Steinhaus?
Hugo Steinhaus Władysław Hugo Dionizy Steinhaus (January 14, 1887 – February 25, 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the Jan Kazimierz University in Lwów (now Lviv, Ukraine), where he helped establish what later became known as the Lwów School of Mathematics. He is credited with "discovering" mathematician Stefan Banach, with whom he gave a notable contribution to functional analysis through the Banach–Steinhaus theorem. After World War II Steinhaus played an important part in the establishment of the mathematics department at Wrocław University and in the revival of Polish mathematics from the destruction of the war.
Schenkerian analysis Schenkerian analysis is a method of musical analysis of tonal music based on the theories of Heinrich Schenker (1868–1935). The goal is to extract the underlying structure of a tonal movement. The basic tenets of the supporing theory can be viewed as a way of defining the way tonality is articulated. A Schenkerian analysis shows hierarchical relationships among pitches, and draws conclusions about the structure of the passage from this hierarchy. The analysis uses a specialized symbolic form of musical notation that Schenker devised to indicate structural status and "prolongation", by which tones that are not contiguous on the surface can nevertheless be connected, and separated by musical material that arises through elaboration on lower structural levels. A key theoretical concept is that of "tonal space"; The intervals between the notes of the tonic triad form a "tonal space" that is filled with passing and neighbour notes, producing new triads and new tonal spaces, open for further elaborations until the surface of the work (the score) is reached.