04/18/2015, 12:24 PM

Currently im considering bases > 2.

I just write exp ignoring the base in notation.

A bundle is a partition of a subset of the complex plane by continu functions that can be ordered.

Consider the bundle ;

Exp^[y](x) for real x and 0 < y < 1

d/dx exp^[y](x) > 0

d^2/d^2x exp^[y](x) > 0

Exp^[y](x) is real-analytic in x.

This bundle is not Unique by those conditions.

The question is , is it Unique by adding ;

Exp^[1/2](- oo ) = c

d/dx exp^[y](1-x) = 1 for 0 < x < 1/2.

??

Existance and uniqueness questions as usual.

Regards

Tommy1729

I just write exp ignoring the base in notation.

A bundle is a partition of a subset of the complex plane by continu functions that can be ordered.

Consider the bundle ;

Exp^[y](x) for real x and 0 < y < 1

d/dx exp^[y](x) > 0

d^2/d^2x exp^[y](x) > 0

Exp^[y](x) is real-analytic in x.

This bundle is not Unique by those conditions.

The question is , is it Unique by adding ;

Exp^[1/2](- oo ) = c

d/dx exp^[y](1-x) = 1 for 0 < x < 1/2.

??

Existance and uniqueness questions as usual.

Regards

Tommy1729