Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For polynomial splines as ll as for Chebyshev splines, it is known that total positivity of the connection matrices is sufficient to obtain B-spline bases.   give a necessary and sufficient condition for the existence of B-bases (or, equivalently, of blossoms) for splines with connection matrices and with sections in different four-dimensional extended Chebyshev spaces.
['Marie-Laurence Mazure']
I am writing a research paper on a idea Chebyshev splines beyond total positivity
[{"from": "human", "value": "I am writing a research paper on a idea Chebyshev splines beyond total positivity"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For polynomial splines as ll as for Chebyshev splines, it is known that total positivity of the connection matrices is sufficient to obtain B-spline bases.   give a necessary and sufficient condition for the existence of B-bases (or, equivalently, of blossoms) for splines with connection matrices and with sections in different four-dimensional extended Chebyshev spaces."}]