Ronald Walker's Research
Much of Dr. Walker's research springs from the field of complex analytic geometry (a subfield of several complex variables), with particular attention to questions relating to complex analytic varieties and their boundaries. (Complex analytic varieties can be viewed as being a special class of "surfaces". The collection of boundaries of analytic varieties can exhibit dramatically different characteristics depending on the nature of the ambient space in which one operates. So identifying which curves bound an analytic variety, and seeing how this depends on the ambient space are some items of interest.) His research of these questions also involves some algebraic geometry and partial differential equations, and has yielded some tangential results in the area of linear dependence. Recent publications include the following:
- Walker R., "Linear dependence of quotients of analytic functions of several variables with the least subcollection of generalized Wronskians," Linear Algebra and its Applications 408 (2005), 151-160.
- Karlovich Y., Spitkovsky I., Walker R., "Almost periodic factorization of block triangular matrix functions revisited," Linear Algebra and its Applications 293 (1999), 199-232.