Abstract:
This thesis contains results about the embeddings of M ̈
untz spaces in the Hilbert
space scenario and its applications to composition operators on M ̈
untz spaces. In the
main, we shall be concerned with the embedding M Λ 2 ⊂ L 2 (μ), where the Hilbert-
M ̈
untz space M Λ 2 is the closed linear span of the monomials x λ n in L 2 ([0, 1]) and μ is
a finite Borel measure on [0, 1].
After gathering together the mathematical preliminaries required for this work
in Chapter 1, we shall use the notion of a sublinear measure introduced by I. Chal-
endar, E. Fricain and D. Timotin [8] to investigate the properties of boundedness,
compactness and belonging to Schatten-von Neumann ideals of these Hilbert space
embeddings. This will be the content of Chapters 2 and 3. In Chapter 4, we give ex-
amples of sublinear measures for bounded and compact embeddings with interesting
properties. Finally, in Chapter 5 the general embedding theory is applied to initiate
the study of composition operators on M Λ 2 .
