Operator algebras of multipliers on reproducing kernel Hilbert spaces

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The aim of my research program is to classify mathematical objects called operators. An operator is a transformation having a very rigid property known as linearity. Plotting the graph of a linear transformation acting on the Cartesian plane results in another plane in three dimensional space, for instance. This simple property of operators makes them amenable to analysis using mathematical tools. On the other hand, operators can be fruitfully used to describe many important phenomena occurring in natural science and engineering. Indeed, they are the basic objects appearing in quantum mechanics for example. Consequently, it is desirable to develop a solid mathematical theory for them. The anticipated classification resulting from my research would yield a convenient method for understanding operators, and could benefit both mathematicians and scientists in other fields.