Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Laplace Subspectrality   Exploring the relationship between geometry and the resonant frequencies of a
shape is of interest to pure and applied mathematicians. These resonant
frequencies are related to the spectrum of the Laplacian, a partial
differential operator. A long-standing research program asks: What geometric
information can one deduce from these harmonics?
  This dissertation explores a related question. Say one shape is subspectral
to another provided each successive resonant frequency of the one is less than
the corresponding frequency of the other. What information can be deduced about
the relationship between the shapes' geometries?
  We use variational arguments to study subspectrality of self-adjoint
operators. We develop analytical tools to study Laplace subspectrality. We then
study subspectrality in rectangles, construct counterexamples in more general
classes of domains, and use the heat trace to relate length subspectrality to
Laplace subspectrality. Finally, we discuss a more general question relating
eigenvalues to functions, stemming from a 1961 conjecture of Polya.

16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat