Who developed one of the foundations of functional analysis and also taught Hugo Steinhaus?
David Hilbert David Hilbert (] ; 23 January 1862 – 14 February 1943) was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
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.